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2 (B) - Newtons Laws of Motion

1) The first document discusses work, energy, and power in the context of mechanics. It provides definitions and formulas to calculate the work done on a mass moving in a gravitational field, as well as the power required to move the mass at a constant speed. 2) The second document describes an experiment to investigate Newton's second law. It involves measuring the acceleration of a trolley pulled by varying weights. The expected graph of acceleration versus weight is proportional. David's data is plotted and used to estimate systematic error, frictional force, and the mass of the trolley. 3) The third document considers the forces on a loaded wheelbarrow. It calculates the minimum vertical force needed to lift the wheel

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0% found this document useful (0 votes)

146 views76 pages

2 (B) - Newtons Laws of Motion

Uploaded by

Aryan Singh

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

You are on page 1/ 76

JAYSHREE PERIWAL INTERNATIONAL SCHOOL

SUB. : PHYSICS TOPIC: MECHANICS

MAY 2003 – HL – PAPER 2 – Q. B 2

1. This question is about work, energy and power.

(a) Define the work done by a force. [2]

.........................................................................

............................................................... ..........

A body of mass m is in a gravitational field of strength g. The body is moved through a distance h at constant
speed v in the opposite direction to the field.

(b) Derive an expression in terms of

(i) m, g and h, for the work done on the body. [2]

............................................................... ......

......................................................... ............

............................................................... ......

(ii) m, g and v, for the power required to move the body. [2]

.....................................................................

............................................................... ......

................................................................... ..

(c) A mass falls near the Earth’s surface at constant speed in still air. Discuss the energy changes, if any, that
occur in the gravitational potential energy and in the kinetic energy of the mass. [3]

............................................................... ..........

.........................................................................

............................................................... ..........

November 2003 – HL – PAPER 2 – Q. A 1

2. This question is about an experiment designed to investigate Newton’s second law.

In order to investigate Newton’s second law, David arranged for a heavy trolley to be accelerated by small
weights, as shown below. The acceleration of the trolley was recorded electronically. David recorded the
acceleration for different weights up to a maximum of 3.0 N. He plotted a graph of his results.

1
acceleration
heavy trolley pulley

weight

(a) Describe the graph that would be expected if two quantities are proportional to one another.

.....................................................................................................................................

.....................................................................................................................................
(2)

(b) David’s data are shown below, with uncertainty limits included for the value of the weights. Draw the best-fit
line for these data.

1.40
acceleration
/ ms–2 1.20

1.00

0.80

0.60

0.40

0.20

0.00
0.00 0.50 1.00 1.50 2.00 2.50
weight / N
(2)

2
(c) Use the graph to

(i) explain what is meant by a systematic error.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) estimate the value of the frictional force that is acting on the trolley.

...........................................................................................................................
(1)

(iii) estimate the mass of the trolley.

...........................................................................................................................

...........................................................................................................................
(2)
(Total 9 marks)

November 2003 – HL - PAPER 2 – Q. B 2 (PART 1)

3. This question is about the forces on a wheelbarrow.

Rachid is using a wheelbarrow to move some blocks. When a lifting force is applied at the handle, its support
legs are lifted off the ground. The dimensions of the wheelbarrow are shown in the diagram below.

When loaded, the total weight of the wheelbarrow and the blocks is 600 N. The ground is horizontal.

(a) Determine,

3
(i) the minimum vertical force needed to lift the support legs off the ground. [3]

............................................. ........................

............................................................... ......

.....................................................................

............................................................... ......

.....................................................................

............................................................... ......

(ii) the magnitude and the direction of the force exerted by the ground on the wheel. [2]

............................................................... ......

.....................................................................

............................................................... ......

.....................................................................

............................................................... ......

.....................................................................

Rachid now pushes the wheelbarrow forward at constant speed. He applies a force of 260 N to the handles at
an angle of 50 to the vertical.

(b) (i) Calculate the horizontal component of the force exerted by Rachid. [2]

.....................................................................

............................................................... ......

.....................................................................

............................................................... ......

(ii) Determine the magnitude of the resultant frictional force acting on the wheelbarrow. [2]

............................................................... ......

.....................................................................

............................................................... ......

................................................................ .....

MAY 2004 – TZ 2 – HL – PAPER 2 – Q. A 2.

4. This question is about the collision between two railway trucks (carts).

(a) Define linear momentum.

.....................................................................................................................................

.....................................................................................................................................
(1)
4
In the diagram below, railway truck A is moving along a horizontal track. It collides with a stationary truck B
and on collision, the two join together. Immediately before the collision, truck A is moving with speed 5.0 ms –
1
. Immediately after collision, the speed of the trucks is v.

5.0 ms –1

B
A

Immediately before collision

B
A

Immediately after collision

The mass of truck A is 800 kg and the mass of truck B is 1200 kg.

(b) (i) Calculate the speed v immediately after the collision.

...........................................................................................................................

...........................................................................................................................
(3)

(ii) Calculate the total kinetic energy lost during the collision.

...........................................................................................................................

........................................................................................................................... (2)

(c) Suggest what has happened to the lost kinetic energy.

.....................................................................................................................................

.....................................................................................................................................
(2)
(Total 8 marks)

MAY 2005 – TZ 1 – HL – PAPER 2 – Q. B1 (PART 1)

5. This question is about momentum and the kinematics of a proposed journey to Jupiter.

(a) State the law of conservation of momentum.

.....................................................................................................................................

5
.....................................................................................................................................
(2)

A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As a result of the
acceleration process, the ions are ejected from the spaceship with a speed of 3.0 × 104 m s–1.

xenon ions spaceship

speed = 3.0×104 m s –1 mass = 5.4×102 kg

(b) The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of xenon is 2.2 × 10 –25
kg.

.....................................................................................................................................

.....................................................................................................................................
(2)

(c) The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 77 × 1018 xenon ions every second, the
fuel will last for 1.5 years. (1 year = 3.2 × 107 s)

.....................................................................................................................................

.....................................................................................................................................
(2)

(d) The mass of the spaceship is 5.4 × 102 kg. Deduce that the initial acceleration of the spaceship is 8.2 × 10–5 m
s–2.

.....................................................................................................................................

.....................................................................................................................................
(5)

The graph below shows the variation with time t of the acceleration a of the spaceship. The solar propulsion
engine is switched on at time t = 0 when the speed of the spaceship is 1.2 × 103 m s–1.

6
10.0

9.5

a / ×10– 5m s– 2
9.0

8.5

8.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0
t / ×107 s

(e) Explain why the acceleration of the spaceship is increasing with time.

.....................................................................................................................................

.....................................................................................................................................
(2)

(f) Using data from the graph, calculate the speed of the spaceship at the time when the xenon fuel has all been
used.

.....................................................................................................................................

.....................................................................................................................................
(4)

(g) The distance of the spaceship from Earth when the solar propulsion engine is switched on is very small compared
to the distance from Earth to Jupiter. The fuel runs out when the spaceship is a distance of 4.7 × 10–11 m from
Jupiter. Estimate the total time that it would take the spaceship to travel from Earth to Jupiter.

.....................................................................................................................................

.....................................................................................................................................
(2)
(Total 19 marks)

7
MAY 2005 – TZ 1 – HL – PAPER 2 – Q. B 4 (PART 1 )

6. This question is about driving a metal bar into the ground and the engine used in the process.

Large metal bars can be driven into the ground using a heavy falling object.

object mass = 2.0×103 kg

bar mass = 400kg

In the situation shown, the object has a mass 2.0 × 103 kg and the metal bar has a mass of 400 kg.

The object strikes the bar at a speed of 6.0 m s–1. It comes to rest on the bar without bouncing. As a result of
the collision, the bar is driven into the ground to a depth of 0.75 m.

(a) Determine the speed of the bar immediately after the object strikes it.

.....................................................................................................................................

.....................................................................................................................................
(4)

(b) Determine the average frictional force exerted by the ground on the bar.

.....................................................................................................................................

.....................................................................................................................................
(3)

8
November 2005 – TZ 0 – HL – PAPER 2 – Q. A2

7. This question is about a balloon used to carry scientific equipment.

The diagram below represents a balloon just before take-off. The balloon’s basket is attached to the ground by
two fixing ropes.

balloon

basket

fixing rope fixing rope

50 50
ground

There is a force F vertically upwards of 2.15  103 N on the balloon. The total mass of the balloon and its
basket is 1.95  102 kg.

(a) State the magnitude of the resultant force on the balloon when it is attached to the ground.

...................................................................................................................................
(1)

(b) Calculate the tension in either of the fixing ropes.

...................................................................................................................................

...................................................................................................................................
(3)

(c) The fixing ropes are released and the balloon accelerates upwards. Calculate the magnitude of this initial
acceleration.

...................................................................................................................................

...................................................................................................................................
(2)

(d) The balloon reaches a terminal speed 10 seconds after take-off. The upward force F remains constant.
9
Describe how the magnitude of air friction on the balloon varies during the first 10 seconds of its flight.

...................................................................................................................................

...................................................................................................................................
(2)
(Total 8 marks)

November 2005 – TZ 0 – HL – PAPER 2 – Q. B 4 (PART 2)

8. Kinematics

(a) State the principle of conservation of energy.

...................................................................................................................................

...................................................................................................................................
(1)

(b) An aircraft accelerates from rest along a hoizontal straight runway and then takes-off. Discuss how the principle
of conservation of energy applies to the energy changes that take place while the aircraft is accelerating along
the runway.

...................................................................................................................................

...................................................................................................................................
(3)

(c) The mass of the aircraft is 8.0  103 kg.

(i) The average resultant force on the aircraft while travelling along the runway is 70 kN. The speed of the
aircraft just as it lifts off is 75 m s–1. Estimate the distance travelled along the runway.

.........................................................................................................................

......................................................................................................................... (3)

(ii) The aircraft climbs to a height of 1250 m. Calculate the potential energy gained during the climb.

.........................................................................................................................

......................................................................................................................... (1)

When approaching its destination, the pilot puts the aircraft into a holding pattern. This means the aircraft flies
at a constant speed of 90 m s–1 in a horizontal circle of radius 500 m as shown in the diagram below.
10
500 m

(d) For the aircraft in the holding pattern,

(i) calculate the magnitude of the resultant force on the aircraft;

.........................................................................................................................

......................................................................................................................... (2)

(ii) state the direction of the resultant force.

.........................................................................................................................

......................................................................................................................... (1)

November 2005 – TZ 0 – SL – PAPER 2 – Q. B 3 (PART 2)

9. Linear momentum

(a) Define

(i) linear momentum;

.........................................................................................................................

......................................................................................................................... (1)

(ii) impulse.

.........................................................................................................................

......................................................................................................................... (1)

(b) Explain whether momentum and impulse are scalar or vector quantities.

...................................................................................................................................

...................................................................................................................................
(1)

...................................................................................................................................

...................................................................................................................................
(5)

A rubber ball of mass 50 g is thrown towards a vertical wall. It strikes the wall at a horizontal speed of 20 m s –

11
1
and bounces back with a horizontal speed of 18 m s–1 as shown below.

speed before = 20 m s –1

speed after =18 m s –1

The ball is in contact with the wall for 0.080 s.

(d) (i) Calculate the change in momentum of the ball.

.........................................................................................................................

.........................................................................................................................
(2)

(ii) Calculate the average force exerted by the ball on the wall.

.........................................................................................................................

.........................................................................................................................
(2)

(iii) Suggest, in terms of Newton’s laws of motion, why a steel ball of the same mass and the same initial
horizontal speed exerts a greater force on the wall.

.........................................................................................................................

.........................................................................................................................
(3)

May 2006 – TZ 2 – HL – PAPER 2 – Q. B 1

10. Mechanical power

(a) Define power.

...................................................................................................................................

...................................................................................................................................
(1)

(b) A car is travelling with constant speed v along a horizontal straight road. There is a total resistive force F

12
acting on the car.

Deduce that the power P to overcome the force F is

P = Fv.

...................................................................................................................................

...................................................................................................................................
(2)

4.80 km

0.30 km

The car moves up the incline at a steady speed of 16 m s−1. During the climb, the average resistive force acting
on the car is 5.0  102 N. The total weight of the car and the driver is 1.2  104 N.

(i) Determine the time it takes the car to travel from the bottom to the top of the incline.

.........................................................................................................................

.........................................................................................................................
(2)

(ii) Determine the work done against the gravitational force in travelling from the bottom to the top of the
incline.

......................................................................................................................... (1)

(iii) Using your answers to (i) and (ii), calculate a value for the minimum power output of the car engine
needed to move the car from the bottom to the top of the incline.

.........................................................................................................................

......................................................................................................................... (4)

(iv) State one reason why your answer to (iii) is only an estimate.

.........................................................................................................................

13
......................................................................................................................... (1)

May 2006 – TZ 1 – HL – PAPER 2 – Q. B 4 (PART 1)

11. Momentum

(a) State the law of conservation of momentum.

...................................................................................................................................

................................................................................................................................... (2)

(b) An ice hockey puck collides with the wall of an ice rink. The puck is sliding along a line that makes an angle
of 45 to the wall.

wall
45 45

ice rink

direction of puck direction of puck

before collision after collision

The collision between the wall and the puck is perfectly elastic.

(i) State what is meant by an elastic collision.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Discuss how the law of conservation of momentum applies to this situation.

.........................................................................................................................

.........................................................................................................................
(2)

Scale: 1.0 cm = 0.10 N s

14
By adding appropriate vectors to the diagram, deduce that the magnitude of the change in momentum of the
puck as a result of the collision is 0.71 N s.
(4)

(d) The sketch-graph below shows the variation with time t of the force F exerted by the wall on the puck.

0
0 t

The total contact time is 12 ms. Estimate, explaining your reasoning, the maximum force exerted by the wall
on the puck.

...................................................................................................................................

...................................................................................................................................
(3)
(Total 12 marks)

November 2006 – TZ 0 – HL – PAPER 2 – Q. B 1 (PART 1)

12. This question is about collisions.

A large metal ball is hung from a crane by means of a cable of length 5.8 m as shown below.

15
cable
crane

5.8 m
wall

metal ball

In order to knock down a wall, the metal ball of mass 350 kg is pulled away from the wall and then released.
The crane does not move. The graph below shows the variation with time t of the speed v of the ball after release.

3.0

2.0
v / m s–1

1.0

0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
t/s

The ball makes contact with the wall when the cable from the crane is vertical.

(a) For the ball just before it hits the wall,

(i) state why the tension in the cable is not equal to the weight of the ball;

.........................................................................................................................

.........................................................................................................................
(1)

(ii) by reference to the graph, estimate the tension in the cable. The acceleration of free fall is 9.8 m s –2.

16
.........................................................................................................................

.........................................................................................................................

.........................................................................................................................
(3)

(b) Use the graph to determine the distance moved by the ball after coming into contact with the wall.

...................................................................................................................................

...................................................................................................................................
(2)

(i) the total change in momentum of the ball;

.........................................................................................................................

.........................................................................................................................
(2)

(ii) the average force exerted by the ball on the wall.

.........................................................................................................................

.........................................................................................................................
(2)

(d) (i) State the law of conservation of momentum.

.........................................................................................................................

......................................................................................................................... (2)

(ii) The metal ball has lost momentum. Discuss whether the law applies to this situation.

.........................................................................................................................

.........................................................................................................................
(2)

(e) During the impact of the ball with the wall, 12 of the total kinetic energy of the ball is converted into thermal
energy in the ball. The metal of the ball has specific heat capacity 450 J kg–1 K–1. Determine the average rise
17
in temperature of the ball as a result of colliding with the wall.

...................................................................................................................................

...................................................................................................................................
(4)
(Total 18 marks)

MAY 2007 – TZ 1 – HL – PAPER 2 – Q. A 2

13. This question is about energy and momentum.

A train carriage A of mass 500 kg is moving horizontally at 6.0 m s –1. It collides with another train carriage B
of mass 700 kg that is initially at rest, as shown in the diagram below.

6.0m s–1

train carriage A train carriage B

500kg 700kg

The graph below shows the variation with time t of the velocities of the two train carriages before, during and
after the collision.

v / ms–1
6.0
train carriage B
5.0

4.0

3.0

2.0

1.0

0.0
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 t / s
–1.0
train carriage A
–2.0

(a) Use the graph to deduce that

(i) the total momentum of the system is conserved in the collision;

.........................................................................................................................
18
.........................................................................................................................

.........................................................................................................................
(2)

(ii) the collision is elastic.

.........................................................................................................................

.........................................................................................................................
(2)

(b) Calculate the magnitude of the average force experienced by train carriage B.

...................................................................................................................................

...................................................................................................................................
(3)
(Total 7 marks)

May 2007 - TZ 1 – SL – PAPER 2 – Q. B 3 (PART 2)

14. Block on an inclined plane

A block is held stationary on a frictionless inclined plane by means of a string as shown below.

string

block

inclined plane

(a) (i) On the diagram draw arrows to represent the three forces acting on the block.
(3)

(ii) The angle  of inclination of the plane is 25. The block has mass 2.6 kg. Calculate the force in the
string. You may assume that g = 9.8 m s–2.

.........................................................................................................................

.........................................................................................................................
(2)

(b) The string is pulled so that the block is now moving at a constant speed of 0.85 m s –1 up the inclined plane.

(i) Explain why the magnitude of the force in the string is the same as that found in (a)(ii).

19
.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) Calculate the power required to move the block at this speed.

.........................................................................................................................

......................................................................................................................... (2)

(iii) State the rate of change of the gravitational potential energy of the block. Explain your answer.

.........................................................................................................................

.........................................................................................................................
(2)
(Total 11 marks)

MAY 2007 – TZ 2 – HL – PAPER 2 – Q. B 1

15. This question is about Newton’s laws of motion, the dynamics of a model helicopter and the engine that
powers it.

(a) Explain how Newton’s third law leads to the concept of conservation of momentum in the collision between
two objects in an isolated system.

...................................................................................................................................

...................................................................................................................................
(4)

(b) The diagram illustrates a model helicopter that is hovering in a stationary position.

0.70 m 0.70 m

rotating
blades

downward motion of air

20
The rotating blades of the helicopter force a column of air to move downwards. Explain how this may enable
the helicopter to remain stationary.

...................................................................................................................................

................................................................................................................................... (3)

(c) The length of each blade of the helicopter in (b) is 0.70 m. Deduce that the area that the blades sweep out as
they rotate is 1.5 m2. (Area of a circle = r2)

...................................................................................................................................

...................................................................................................................................
(1)

(d) For the hovering helicopter in (b), it is assumed that all the air beneath the blades is pushed vertically
downwards with the same speed of 4.0 m s–1. No other air is disturbed.

The density of the air is 1.2 kg m–3.

Calculate, for the air moved downwards by the rotating blades,

(i) the mass per second;

.........................................................................................................................

.........................................................................................................................
(2)

(ii) the rate of change of momentum.

.........................................................................................................................

.........................................................................................................................
(1)

(e) State the magnitude of the force that the air beneath the blades exerts on the blades.

...................................................................................................................................
(1)

(f) Calculate the mass of the helicopter and its load.

...................................................................................................................................

21
...................................................................................................................................
(2)

(g) In order to move forward, the helicopter blades are made to incline at an angle  to the horizontal as shown
schematically below.

While moving forward, the helicopter does not move vertically up or down. In the space provided below draw
a free body force diagram that shows the forces acting on the helicopter blades at the moment that the
helicopter starts to move forward. On your diagram, label the angle .
(4)

(h) Use your diagram in (g) opposite to explain why a forward force F now acts on the helicopter and deduce that
the initial acceleration a of the helicopter is given by

a = g tan 

where g is the acceleration of free fall.

...................................................................................................................................

...................................................................................................................................
(5)

(i) Suggest why, even though the forward force F does not change, the acceleration of the helicopter will
decrease to zero as it moves forward.

...................................................................................................................................

...................................................................................................................................
(2)

November 2007 – TZ 0 – HL – PAPER 2 – Q. B2 (PART 1)

16. Momentum

(a) State the law of conservation of linear momentum.

...................................................................................................................................

...................................................................................................................................
22
...................................................................................................................................
(2)

(b) A toy rocket of mass 0.12 kg contains 0.59 kg of water as shown in the diagram below.

high-pressure air

water

nozzle, radius 1.4mm

The space above the water contains high-pressure air. The nozzle of the rocket has a circular cross-section of
radius 1.4 mm. When the nozzle is opened, water emerges from the nozzle at a constant speed of 18 m s–1.
The density of water is 1000 kg m–3.

(i) Deduce that the volume of water ejected per second through the nozzle is 1.1  10–4 m3.

.........................................................................................................................

.........................................................................................................................
(2)

(ii) Deduce that the upward force that the ejected water exerts on the rocket is approximately 2.0 N. Explain your
working by reference to Newton’s laws of motion.

.........................................................................................................................

.........................................................................................................................
(4)

(iii) Calculate the time delay between opening the nozzle and the rocket achieving lift-off.

.........................................................................................................................

.........................................................................................................................
(2)

MAY 2008 – TZ 2 – SL – PAPER 2 – Q. A 3

17. Two identical springs A and B each have a force constant (force per unit extension) of 2.5Ncm –1. One end of
each spring is attached to a trolley and the other ends are attached to rigid supports, as shown.

23
support trolley

spring A spring B

The springs are horizontal and, when the trolley is at rest, the extension of each spring is 3.0 cm. The trolley is
displaced 1.2 cm to the right.

support trolley

spring A spring B

displacement 1.2 cm

(a) Calculate the magnitude of the force on the trolley due to

(i) spring A alone.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) spring B alone.

...........................................................................................................................

...........................................................................................................................
(1)

(b) The trolley is released. Determine the initial acceleration of the trolley of mass 0.75 kg.

.....................................................................................................................................

.....................................................................................................................................
(2)
(Total 5 marks)

MAY 2008 – TZ 2 – HL – PAPER 2 – Q. B 1 (PART 1)

18. This question is about units and momentum.

(a) Distinguish between fundamental units and derived units.

.....................................................................................................................................

.....................................................................................................................................
(1)

24
(b) The rate of change of momentum R of an object moving at speed v in a stationary fluid of constant density is
given by the expression

R = kv2

where k is a constant.

(i) State the derived units of speed v.

...........................................................................................................................
(1)

(ii) Determine the derived units of R.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) Use the expression and your answers in (b)(i) and (b)(ii) to determine the derived units of k.

...........................................................................................................................

...........................................................................................................................
(1)

(i) linear momentum.

...........................................................................................................................

...........................................................................................................................
(1)

(ii) impulse.

...........................................................................................................................

...........................................................................................................................
(1)

(d) In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed of 18 m s–1. It passes
through a shallow tank containing stationary water. The tank is of length 9.3 m. The carriage leaves the tank at
a speed of 13 m s–1.

18 m s–1 water-tank 13 m s–1

carriage, mass 450 kg

9.3m

As the carriage passes through the tank, the carriage loses momentum and causes some water to be pushed
forwards with a speed of 19 m s–1 in the direction of motion of the carriage.

25
(i) For the carriage passing through the water-tank, deduce that the magnitude of its total change in momentum is
2250N s.

...........................................................................................................................

...........................................................................................................................
(1)

(ii) Use the answer in (d)(i) to deduce that the mass of water moved in the direction of motion of the carriage is
approximately 120 kg.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) Calculate the mean value of the magnitude of the acceleration of the carriage in the water.

...........................................................................................................................

...........................................................................................................................
(3)

(e) For the carriage in (d) passing through the water-tank, determine

(i) its total loss in kinetic energy.

...........................................................................................................................

...........................................................................................................................
(3)

(ii) the gain in kinetic energy of the water that is moved in the direction of motion of the carriage.

...........................................................................................................................

...........................................................................................................................
(1)

(f) By reference to the principles of conservation of momentum and of energy, explain your answers in (e).

.....................................................................................................................................

.....................................................................................................................................
(3)
(Total 20 marks)

MAY 2008 – TZ 1 – SL – PAPER 2 – Q. A 3

26
19. This question is about the breaking distance of a car and specific heat capacity.

(a) A car of mass 960 kg is free-wheeling down an incline at a constant speed of 9.0 m s–1.

speed = 9.0 m s -1

15

The slope makes an angle of 15° with the horizontal.

(i) Deduce that the average resistive force acting on the car is 2.4×103N.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Calculate the kinetic energy of the car.

...........................................................................................................................

...........................................................................................................................
(1)

(b) The driver now applies the brakes and the car comes to rest in 15 m. Use your answer to (a)(ii) to calculate the
average braking force exerted on the car in coming to rest.

.....................................................................................................................................

.....................................................................................................................................
(2)

(c) The same braking force is applied to each rear wheel of the car. The effective mass of each brake is 5.2 kg with
a specific heat capacity of 900 J kg–1 K–1. Estimate the rise in temperature of a brake as the car comes to rest.
State one assumption that you make in your estimation.

estimate:

.....................................................................................................................................

.....................................................................................................................................
27
.....................................................................................................................................

.....................................................................................................................................

assumption:

.....................................................................................................................................

.....................................................................................................................................
(4)
(Total 9 marks)

MAY 2008 – TZ 1 – HL – PAPER 2 – Q. B 1 (PART 1 )

20. This question is about momentum and energy.

(a) Define impulse of a force and state the relation between impulse and momentum.

definition:

.....................................................................................................................................

relation:

.....................................................................................................................................

.....................................................................................................................................
(2)

(b) By applying Newton’s laws of motion to the collision of two particles, deduce that momentum is conserved in
the collision.

.....................................................................................................................................

.....................................................................................................................................
(5)

(c) In an experiment to measure the speed of a bullet, the bullet is fired into a piece of plasticine suspended from a
rigid support by a light thread.

28
24cm
bullet
speed V

plasticine

The speed of the bullet on impact with the plasticine is V. As a result of the impact, the bullet embeds itself in
the plasticine and the plasticine is displaced vertically through a height of 24 cm. The mass of the bullet is
5.2×10–3 kg and the mass of the plasticine is 0.38 kg.

(i) Ignoring the mass of the bullet, calculate the speed of the plasticine immediately after the impact.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Deduce that the speed V with which the bullet strikes the plasticine is about 160 m s–1.

...........................................................................................................................

...........................................................................................................................
(2)
(Total 11 marks)

MAY 2008 – TZ 1 – SL – PAPER 2 – Q. B 2 (PART 1)

21. This question is about power.

(a) Define power.

.....................................................................................................................................

.....................................................................................................................................
(1)

(b) A constant force of magnitude F moves an object at constant speed v in the direction of the force. Deduce that
the power P required to maintain constant speed is given by the expression

P = Fv

.....................................................................................................................................

29
.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................
(2)

(c) Sand falls vertically on to a horizontal conveyor belt at a rate of 60 kg s–1.

sand
60 kg s-1
2.0 m s-1

The conveyor belt that is driven by an engine, moves with speed 2.0 m s–1.

When the sand hits the conveyor belt, its horizontal speed is zero.

(i) Identify the force F that accelerates the sand to the speed of the conveyor belt.

...........................................................................................................................
(1)

(ii) Determine the magnitude of the force F.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) Calculate the power P required to move the conveyor belt at constant speed.

...........................................................................................................................

...........................................................................................................................
(1)

(iv) Determine the rate of change of kinetic energy K of the sand.

...........................................................................................................................

...........................................................................................................................
(2)

(v) Explain why P and K are not equal.

30
...........................................................................................................................

...........................................................................................................................

...........................................................................................................................
(2)

(d) The engine that drives the conveyor belt has an efficiency of 40%. Calculate the input power to the engine.

.....................................................................................................................................

.....................................................................................................................................
(2)

(Total 13 marks)

November 2008 – TZ 0 – HL – PAPER 2 – Q. A 2

22. This question is about momentum.

(a) A rocket in outer space far from any other masses is used to propel a satellite. At t=0 the engines are turned on and gases
leave the rear of the rocket with speed v relative to the rocket.

(i) Explain, in terms of Newton’s laws of motion, why the rocket will accelerate. [2]

......................................................................................................................................

(ii) Outline how the law of conservation of momentum applies to the motion of the rocket. [2]

......................................................................................................................................

(iii) The gases leave the rear of the rocket at a constant rate of R kg per second. The mass of the rocket (including fuel)
at t=0 is M.
Deduce that the initial acceleration, a, of the rocket is given by the expression
R
a= v
M

......................................................................................................................................

31
......................................................................................................................................

......................................................................................................................................

(b) The diagram below shows a two-stage rocket that is used to accelerate a satellite that has the same mass as in (a). The
rocket has the same mass as the single stage rocket and carries the same mass of fuel as in (a).

Each stage is discarded after all its fuel has been used. Explain, using the answer in (a)(iii), whether the final speed of the
satellite will be larger, equal or smaller than that of the satellite accelerated by the single stage rocket. [2]

......................................................................................................................................

MAY 2009 – TZ 1 – HL – PAPER 2 – Q. A 2

23. This question is about impulse.

(a) A net force of magnitude F acts on a body. Define the impulse I of the force.

......................................................................................................................................

...................................................................................................................................... (1)

(b) A ball of mass 0.0750 kg is travelling horizontally with a speed of 2.20 m s –1. It strikes a vertical wall and
rebounds horizontally.

Due to the collision with the wall, 20 % of the ball’s initial kinetic energy is dissipated.

(i) Show that the ball rebounds from the wall with a speed of 1.97 m s –1.

...........................................................................................................................
32
...........................................................................................................................

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Show that the impulse given to the ball by the wall is 0.313 N s.

...........................................................................................................................

...........................................................................................................................
(2)

The sketch graph shows how the force F that the wall exerts on the ball is assumed to vary with time t.

The time T is measured electronically to equal 0.0894 s.

Use the impulse given in (b)(ii) to estimate the average value of F.

......................................................................................................................................

......................................................................................................................................
(4)
(Total 9 marks)

MAY 2009 – TZ 1 – SL – PAPER 2 – Q. B 1 (PART 2)

24. This question is about motion of a ball falling in oil.

(a) Distinguish between average speed and instantaneous speed.

......................................................................................................................................

......................................................................................................................................
33
......................................................................................................................................
(2)

(b) A small steel ball of mass M is dropped from rest into a long vertical tube that contains oil.

The sketch graph shows how the speed v of the ball varies with time t.

Explain how you would use the graph to find the average speed of the ball between t = 0 and t = t1.

......................................................................................................................................

......................................................................................................................................
(3)

(c) The gradient of the graph at t = t1 is k. Deduce an expression in terms of k, M and g, the acceleration of free
fall, for the magnitude of the frictional force F acting on the ball at t = t1.

......................................................................................................................................

......................................................................................................................................
(3)

(d) State and explain the magnitude of the frictional force acting on the ball at t = t2.

......................................................................................................................................

......................................................................................................................................
(3)
(Total 11 marks)

34
MAY 2009 – TZ 2 – HL – PAPER 2 – Q. B 1 (PART 1)

25. This question is about dynamics and energy.

A bullet of mass 32 g is fired from a gun. The graph shows the variation of the force F on the bullet with time t
as it travels along the barrel of the gun.

The bullet is fired at time t = 0 and the length of the barrel is 0.70 m.

1 2
(a) State and explain why it is inappropriate to use the equation s = ut + at to calculate the acceleration of the
2
bullet.

......................................................................................................................................

......................................................................................................................................
(2)

(b) Use the graph to

(i) determine the average acceleration of the bullet during the final 2.0 ms of the graph.

...........................................................................................................................
35
...........................................................................................................................

...........................................................................................................................

...........................................................................................................................
(2)

(ii) show that the change in momentum of the bullet, as the bullet travels along the length of the barrel, is
approximately 9 N s.

...........................................................................................................................

...........................................................................................................................
(3)

(c) Use the answer in (b)(ii) to calculate the

(i) speed of the bullet as it leaves the barrel.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) average power delivered to the bullet.

...........................................................................................................................

...........................................................................................................................
(3)

(d) Use Newton’s third law to explain why a gun will recoil when a bullet is fired.

......................................................................................................................................

36
......................................................................................................................................
(3)
(Total 15 marks)

November 2009 – TZ 2 – SL – PAPER 2 – Q. B 1 (PART 2)

26. This question is about force and energies.

(a) A system consists of a bicycle and cyclist travelling at a constant velocity along a horizontal road.

(i) State the value of the net force acting on the cyclist.

...........................................................................................................................
(1)

(ii) On the diagram draw labelled arrows to represent the vertical forces acting on the bicycle.
(2)

(iii) With reference to the horizontal forces acting on the system, explain why the system is travelling at constant
velocity.

...........................................................................................................................

...........................................................................................................................
(2)

(b) The total resistive force acting on the system is 40 N and its speed is 8.0 m s–1. Calculate the useful power
output of the cyclist.

......................................................................................................................................

......................................................................................................................................
(1)
37
(c) The cyclist stops pedalling and the system comes to rest. The total mass of the system is 70 kg.

(i) Calculate the magnitude of the initial acceleration of the system.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Estimate the distance taken by the system to come to rest from the time the cyclist stops pedalling.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) State and explain one reason why your answer to (c)(ii) is only an estimate.

...........................................................................................................................

...........................................................................................................................
(2)
(Total 12 marks)
November 2009 – TZ 0 – HL – PAPER 2 – Q .A 5
27. This question is about forces.

A solid iron ball of mass 770 kg is used on a building site. The ball is suspended by a rope from a crane. The
distance from the point of suspension to the centre of mass of the ball is 12 m.

(a) Calculate the tension in the rope when the ball hangs vertical and stationary.

......................................................................................................................................

......................................................................................................................................
(1)

(b) The ball is pulled back from the vertical and then released. It falls through a vertical height of 1.6 m and
strikes a wall.

38
(i) Calculate the speed of the ball just before impact.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Calculate the tension in the rope just before impact.

...........................................................................................................................

...........................................................................................................................
(3)

(c) The ball is brought to rest in 0.15 s. The sketch graph below shows how the force the ball exerts on the wall
varies with time.

(i) State what quantity is represented by the area under the graph.

...........................................................................................................................
(1)

(ii) Determine the maximum force Fmax exerted by the ball on the wall.

...........................................................................................................................

...........................................................................................................................
(3)
(Total 10 marks)

MAY 2010 – TZ 1 – HL – PAPER 2 – Q. A 2

28. This question is about forces.

39
An athlete trains by dragging a heavy load across a rough horizontal surface.

The athlete exerts a force of magnitude F on the load at an angle of 25° to the horizontal.

(a) Once the load is moving at a steady speed, the average horizontal frictional force acting on the load is 470 N.

Calculate the average value of F that will enable the load to move at constant speed.

......................................................................................................................................

......................................................................................................................................
(2)

(b) The load is moved a horizontal distance of 2.5 km in 1.2 hours.

Calculate

(i) the work done on the load by the force F.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) the minimum average power required to move the load.

...........................................................................................................................

...........................................................................................................................
(2)

Explain, in terms of energy changes, why the minimum average power required is greater than in (b)(ii).

......................................................................................................................................

......................................................................................................................................
(2)
(Total 8 marks)

40
MAY 2010 – TZ 1 – SL – PAPER 2 – Q. B 1 ( PART 2)

29. This question is about kicking a football.

A ball is suspended from a ceiling by a string of length 7.5 m. The ball is kicked horizontally and rises to a
maximum height of 6.0 m.

(a) Assuming that the air resistance is negligible, show that the initial speed of the ball is 11 m s–1.

......................................................................................................................................

......................................................................................................................................
(2)

(b) The mass of the ball is 0.55 kg and the impact time of the kicker’s foot with the ball is 150 ms. Estimate the
average force exerted on the ball by the kick.

......................................................................................................................................

......................................................................................................................................
(2)

...........................................................................................................................

...........................................................................................................................
(3)

(ii) Calculate the tension in the string immediately after the ball is kicked. Assume that the string is vertical.

...........................................................................................................................

...........................................................................................................................
41
(3)
(Total 10 marks)

MAY 2010 – TZ 2 – HL – PAPER 2 – Q. B 4 (PART 1 )

30. This question is about momentum, energy and power.

(a) In his Principia Mathematica Newton expressed his third law of motion as “to every action there is always
opposed an equal reaction”. State what Newton meant by this law.

......................................................................................................................................

......................................................................................................................................
(1)

(b) A book is released from rest and falls towards the surface of Earth. Discuss how the conservation of
momentum applies to the Earth-book system.

......................................................................................................................................

......................................................................................................................................
(3)

(c) A large swinging ball is used to drive a horizontal iron spike into a vertical wall.
The centre of the ball falls through a vertical height of 1.6 m before striking the spike in the position shown.

The mass of the ball is 3.5 kg and the mass of the spike is 0.80 kg. Immediately after striking the spike, the
ball and spike move together. Show that the

(i) speed of the ball on striking the spike is 5.6 m s–1.

...........................................................................................................................

...........................................................................................................................
42
........................................................................................................................... (1)

(ii) energy dissipated as a result of the collision is about 10 J.

...........................................................................................................................

...........................................................................................................................
(4)

(d) As a result of the ball striking the spike, the spike is driven a distance 7.3 × 10–2 m into the wall. Calculate,
assuming it to be constant, the friction force F between the spike and wall.

......................................................................................................................................

......................................................................................................................................
(3)

(e) The machine that is used to raise the ball has a useful power output of 18 W. Calculate how long it takes for
the machine to raise the ball through a height of 1.6 m.

......................................................................................................................................

......................................................................................................................................
(3)
November 2010 – TZ 0 – HL – PAPER 2 – Q. B 4

31. This question is about collisions.

(a) Sate the principle of conservation of momentum

......................................................................................................................................

(b) In an experiment, an air-rifle pellet is fired into a block of modelling clay that rests on a table.

43
The air-rifle pellet remains inside the clay block after the impact.

As a result of the collision, the clay block slides along the table in a straight line and comes to rest.
Further data relating to the experiment are given below.

Mass of air-rifle pellet = 2.0 g

Mass of clay block = 56 g
Velocity of impact of air-rifle pellet =140 m s–1
Stopping distance of clay block = 2.8 m

(i) Show that the initial speed of the clay block after the air-rifle pellet strikes it is 4.8 m s–1. [2]

......................................................................................................................................

(ii) Calculate the average frictional force that the surface of the table exerts on the clay block whilst the clay
block is moving. [4]

......................................................................................................................................

(c) The experiment is repeated with the clay block placed at the edge of the table so that it is fired away from
the table. The initial speed of the clay block is 4.3 m s–1 horizontally. The table surface is 0.85 m above
the ground.

44
(i) Ignoring air resistance, calculate the horizontal distance travelled by the clay block before it strikes the
ground. [4]

......................................................................................................................................

(ii) The diagram in (c) shows the path of the clay block neglecting air resistance. On the diagram, draw the
approximate shape of the path that the clay block will take assuming that air resistance acts on the clay
block. [3]

MAY 2011 – TZ 1 – HL – PAPER 2 – Q. B 2 ( PART 1 )

32. This question is about mechanics and thermal physics.

The graph shows the variation with time t of the speed v of a ball of mass 0.50 kg that has been released from
rest above the Earth’s surface.

45
The force of air resistance is not negligible. Assume that the acceleration of free fall is g = 9.81 m s–2.

(a) State, without any calculations, how the graph could be used to determine the distance fallen.

......................................................................................................................................

......................................................................................................................................
(1)

(b) (i) In the space below, draw and label arrows to represent the forces on the ball at 2.0 s.

(1)

(ii) Use the graph opposite to show that the acceleration of the ball at 2.0 s is approximately 4 m s–2.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) Calculate the magnitude of the force of air resistance on the ball at 2.0 s.

...........................................................................................................................

46
...........................................................................................................................

...........................................................................................................................
(2)

(iv) State and explain whether the air resistance on the ball at t = 5.0 s is smaller than, equal to or greater than the
air resistance at t = 2.0 s.

...........................................................................................................................

...........................................................................................................................
(2)

(c) After 10 s the ball has fallen 190 m.

(i) Show that the sum of the potential and kinetic energies of the ball has decreased by 780 J.

...........................................................................................................................

...........................................................................................................................
(3)

(ii) The specific heat capacity of the ball is 480 J kg–1 K–1. Estimate the increase in the temperature of the ball.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) State an assumption made in the estimate in (c)(ii).

...........................................................................................................................

...........................................................................................................................
(1)
(Total 14 marks)

MAY 2011 – TZ 1 – HL – PAPER 2 – Q. B 2 (PART 1)

33. This question is about mechanics and thermal physics.

The graph shows the variation with time t of the speed v of a ball of mass 0.50 kg, that has been released from
rest above the Earth’s surface.
47
The force of air resistance is not negligible. Assume that the acceleration of free fall is g = 9.81ms−2.

(a) State, without any calculations, how the graph could be used to determine the distance fallen. [1]

......................................................................................................................................

(b) (i) In the space below, draw and label arrows to represent the forces on the ball at 2.0 s. [1]

(ii) Use the graph opposite to show that the acceleration of the ball at 2.0 s is approximately 4ms−2. [2]

......................................................................................................................................

48
......................................................................................................................................

......................................................................................................................................

(iii) Calculate the magnitude of the force of air resistance on the ball at 2.0 s. [2]

......................................................................................................................................

(iv) State and explain whether the air resistance on the ball at t = 5.0 s is smaller than, equal to or greater
than the air resistance at t = 2.0 s. [2]

......................................................................................................................................

(c) After 10 s the ball has fallen 190 m.

(i) Show that the sum of the potential and kinetic energies of the ball has decreased by 780 J. [3]

......................................................................................................................................

(ii) The specific heat capacity of the ball is 480 J kg−1 K−1. Estimate the increase in the temperature of the
ball. [2]

......................................................................................................................................

......................................................................................................................................
49
(iii) State an assumption made in the estimate in (c)(ii). [1]

......................................................................................................................................

MAY 2011 – TZ 2 – HL – PAPER 2 – Q. B 3 (PART 1)

34. This question is about power and efficiency.

A bus is travelling at a constant speed of 6.2 m s–1 along a section of road that is inclined at an angle of 6.0° to
the horizontal.

(a) (i) The bus is represented by the black dot shown below. Draw a labelled sketch to represent the forces
acting on the bus.

(4)

(ii) State the value of the rate of change of momentum of the bus.

...........................................................................................................................
(1)

(b) The total output power of the engine of the bus is 70 kW and the efficiency of the engine is 35 %. Calculate
the input power to the engine.

......................................................................................................................................

50
......................................................................................................................................
(2)

......................................................................................................................................

......................................................................................................................................
(3)

(d) Using your answer to (c) and the data in (b), estimate the magnitude of the resistive forces acting on the bus.

......................................................................................................................................

......................................................................................................................................
(3)

(e) The engine of the bus suddenly stops working.

(i) Determine the magnitude of the net force opposing the motion of the bus at the instant at which the
engine stops.

...........................................................................................................................

...........................................................................................................................
(2)

(ii) Discuss, with reference to the air resistance, the change in the net force as the bus slows down.

...........................................................................................................................

...........................................................................................................................
(2)
(Total 17 marks)

MAY 2012 – TZ 1 – HL – PAPER 2 – Q. B 3 (PART 1)

35. This question is about a collision.

Two identical blocks of mass 0.17 kg and length 0.050 m are travelling towards each other along a
straight line through their centres as shown below. Assume that the surface is frictionless.

51
The initial distance between the centres of the blocks is 0.900 m and both blocks are moving at a
speed of 0.18 m s–1 relative to the surface.
(a) Determine the time taken for the blocks to come into contact with each other. [3]

(b) As a result of the collision, the blocks reverse their direction of motion and travel at the same speed
as each other. During the collision, 20 % of the kinetic energy of the blocks is given off as thermal
energy to the surroundings.
(i) State and explain whether the collision is elastic or inelastic. [2]

………………………………………………………………………………………………………………

……………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(ii) Show that the final speed of the blocks relative to the surface is 0.16 m s–1. [3]

………………………………………………………………………………………………………………

……………………………………………………………………………………………………………

………………………………………………………………………………………………………………

……………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(c) (i) State Newton’s third law of motion. [1]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(ii) During the collision of the blocks, the magnitude of the force that block A exerts on block B is
FAB and the magnitude of the force that block B exerts on block A is FBA. On the diagram
below, draw labelled arrows to represent the magnitude and direction of the forces FAB and FBA.
[3]

52
(iii) The duration of the collision between the blocks is 0.070 s. Determine the average force one
block exerted on the other. [3]

………………………………………………………………………………………………………………

MAY 2012 – TZ 2 – HL – PAPER 2 – Q. B 3 (PART 1)

36. This question is about kinematics and mechanics.

(a) Define linear momentum. [1]

………………………………………………………………………………………………………………

(b) State, in terms of momentum, Newton’s second law of motion. [1]

………………………………………………………………………………………………………………

(c) Show, using your answer to (b), how the impulse of a force F is related to the change in momentum Δ
p that it produces. [1]

………………………………………………………………………………………………………………

(d) A railway truck on a level, straight track is initially at rest. The truck is given a quick, horizontal push
by an engine so that it now rolls along the track.

53
The engine is in contact with the truck for a time T = 0.54 s and the initial speed of the truck after the
push is 4.3 m s–1. The mass of the truck is 2.2 ×103 kg.

Due to the push, a force of magnitude F is exerted by the engine on the truck. The sketch shows how
F varies with contact time t.

(i) Determine the magnitude of the maximum force Fmax exerted by the engine on the truck. [4]

………………………………………………………………………………………………………………

(ii) After contact with the engine (t = 0.54 s) the truck moves a distance 15 m along the track.
After travelling this distance the speed of the truck is 2.8 m s–1. Assuming a uniform
acceleration, calculate the time it takes the truck to travel 15 m. [2]

………………………………………………………………………………………………………………

54
(iii) Calculate the average rate at which the kinetic energy of the truck is dissipated as it moves
along the track. [2]

………………………………………………………………………………………………………………

(iv) When the speed of the truck is 2.8 m s–1 it collides with a stationary truck of mass 3.0 ×103 kg.
The two trucks move off together with a speed V. Show that the speed V = 1.2 m s–1. [2]

………………………………………………………………………………………………………………

(v) Outline the energy transformations that take place during the collision of the two trucks. [2]

………………………………………………………………………………………………………………

November 2012 – TZ 0 – HL – PAPER 2 – Q. A2

37. This question is about momentum change.

(a) State the law of conservation of linear momentum. [2]

………………………………………………………………………………………………………………

(b) Gravel falls vertically onto a moving horizontal conveyor belt.

55
(i) The gravel falls at a constant rate of 13 kg s–1 through a height of 1.9 m. Show that the vertical speed
of the gravel as it lands on the conveyor belt is about 6 m s–1. [2]

………………………………………………………………………………………………………………

(ii) The gravel lands on the conveyor belt without rebounding. Calculate the rate of change of the vertical
momentum of the gravel. [2]

………………………………………………………………………………………………………………

(iii) Gravel first reaches the belt at t = 0.0 s and continues to fall. Determine the total vertical force that
the gravel exerts on the conveyor belt at t = 5.0 s. [3]

………………………………………………………………………………………………………………

(c) The conveyor belt moves with a constant horizontal speed of 1.5 m s–1. As the gravel lands on the
belt, it has no horizontal speed.

(i) Calculate the rate of change of the kinetic energy of the gravel due to its change in horizontal
speed. [1]

………………………………………………………………………………………………………………

(ii) Determine the power required to move the conveyor belt at constant speed. [2]

………………………………………………………………………………………………………………
56
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(iii) Outline why the answers to (c)(i) and (ii) are different. [1]

………………………………………………………………………………………………………………

MAY 2013 – TZ 1 – HL – PAPER 2 – Q. A 4

38. This question is about impulse and momentum.

The diagram shows an arrangement used to test golf club heads.

The shaft of a club is pivoted and the centre of mass of the club head is raised by a height h before
being released. On reaching the vertical position the club head strikes the ball.
(a) (i) Describe the energy changes that take place in the club head from the instant the club is
released until the club head and the ball separate. [2]

………………………………………………………………………………………………………………

(ii) Calculate the maximum speed of the club head achievable when h = 0.85 m. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
57
(b) The diagram shows the deformation of a golf ball and club head as they collide during a test.

Explain how increasing the deformation of the club head may be expected to increase the speed at
which the ball leaves the club. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(c) In a different experimental arrangement, the club head is in contact with the ball for a time of 220 μs.
The club head has mass 0.17 kg and the ball has mass 0.045 kg. At the moment of contact the ball is
at rest and the club head is moving with a speed of 38 m s–1. The ball moves off with an initial speed
of 63 m s–1.
(i) Calculate the average force acting on the ball while the club head is in contact with the ball.

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(ii) State the average force acting on the club head while it is in contact with the ball. [1]

………………………………………………………………………………………………………………

(iii) Calculate the speed of the club head at the instant that it loses contact with the ball. [2]

………………………………………………………………………………………………………………

MAY 2013 – TZ 2 – HL – PAPER 2 – Q. B 4 (PART 2)

39. This question is about momentum and energy.

(a) Define linear momentum. [1]

58
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(b) State the law of conservation of momentum. [2]

………………………………………………………………………………………………………………

The engines of the space rocket are turned on and it accelerates by burning fuel and ejecting gases. Discuss
how the law of conservation of momentum relates to this situation. [3]

………………………………………………………………………………………………………………

(d) Jane and Joe are two ice skaters initially at rest on a horizontal skating rink. They are facing each other and
Jane is holding a ball. Jane throws the ball to Joe who catches it. The speed at which the ball leaves Jane,
measured relative to the ground, is 8.0 m s–1.

The following data are available.

Mass of Jane = 52 kg

Mass of Joe = 74 kg

Mass of ball = 1.3 kg

Use the data to calculate the

(i) speed v of Jane relative to the ground immediately after she throws the ball. [2]

………………………………………………………………………………………………………………

(ii) speed V of Joe relative to the ground immediately after he catches the ball. [2]

………………………………………………………………………………………………………………

59
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(e) Jane and Joe are initially separated by 4.0 m. The average frictional force between their skates and the ice is
0.12 N. Show that the separation of Jane and Joe after the ball is thrown and they are at rest again is about 20
m. [5]

………………………………………………………………………………………………………………

November 2013 – TZ 0 – SL – PAPER 2 – Q .1

40. This question is about forces.

A stone block is pulled at constant speed up an incline by a cable attached to an electric motor.

60
The incline makes an angle of 12 with the horizontal. The weight of the block is 1.5×104 N and the tension T
in the cable is 4.2×103 N.

(a) On the diagram draw and label arrows that represent the forces acting on the block. [2]

(b) Calculate the magnitude of the friction force acting on the block. [3]

………………………………………………………………………………………………………………

November 2013 – TZ 0 – HL – PAPER 2 – Q. 9

41. This question is about Newton’s laws and momentum.

(a) State the condition for the momentum of a system to be conserved. [1]

………………………………………………………………………………………………………………

(b) A person standing on a frozen pond throws a ball. Air resistance and friction can be considered to be
negligible.
(i) Outline how Newton’s third law and the conservation of momentum apply as the ball is thrown. [3]

61
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(ii) Explain, with reference to Newton’s second law, why the horizontal momentum of the ball remains
constant whilst the ball is in flight. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(c) The maximum useful power output of a locomotive engine is 0.75 MW. The maximum speed of the
locomotive as it travels along a straight horizontal track is 44 m s–1.
Calculate the frictional force acting on the locomotive at this speed. [2]
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(d) The locomotive engine in (c) gives a truck X a sharp push such that X moves along a horizontal track
and collides with a stationary truck Y. As a result of the collision the two trucks stick together and
move off with speed v. The following data are available.
Mass of truck X =3.7×103 kg
Mass of truck Y =6.3×103 kg
Speed of X just before collision =4.0 m s–1

(i) Calculate v. [2]

………………………………………………………………………………………………………………

(ii) Determine the kinetic energy lost as a result of the collision. [2]
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

62
………………………………………………………………………………………………………………
(e) The trucks X and Y come to rest after travelling a distance of 40 m along the horizontal track.
Determine the average frictional force acting on X and Y. [3]

………………………………………………………………………………………………………………

November 2014 – TZ 0 – SL – PAPER 2 – Q. 4 (PART 1)

42. This question is about the motion of a ship and observing objects from it.

(a) Outline the meaning of work. [2]

………………………………………………………………………………………………………………

(b) Some cargo ships use kites working together with the ship’s engines to move the vessel.

The tension in the cable that connects the kite to the ship is 250 kN. The kite is pulling the ship at an angle of
39 to the horizontal. The ship travels at a steady speed of 8.5 m s – 1 when the ship’s engines operate with a
power output of 2.7 MW.

(i) Calculate the work done one the shop by the kite when the ship travels a distance of 1.0 km. [2]

………………………………………………………………………………………………………………

(ii) Show that, when the ship is travelling at a speed of 8.5 m s – 1, the kite provides about 40% of the total power
required by the ship. [4]

63
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(c) The kite is taken down and no longer produces a force on the ship. The resistive force F that opposes the
motion of the ship is related to the speed v of the ship by

F = kv3

Where k is constant

Show that, if the power output of the engines remains at 2.7 MW, the speed of the ship will decrease to 7 m s –
1
. Assume that k is independent of whether the kite is in use or not. [3]

………………………………………………………………………………………………………………

(d) The ship’s enginges are switched off and the ship comes to rest from a speed of 7 m s – 1 in a time of 650 s.

(i) Esitmate the distance that the ship takes to stop. Assume that the acceleration is uniform. [2]

………………………………………………………………………………………………………………

(ii) It is unlikely that the acceleration of the ship will be uniform given that the resistive force acting on the ship
depends on the speed of the shop. Using the axes, sketch a graph to show how the speed v varies with time t
after the ship’s engines are switched off. [2]

64
MAY 2015 – TZ 2 – HL – Q 8. (PART 2)

43. This question is about momentum.

(a) State the law of conservation of linear momentum. [2]

………………………………………………………………………………………………………………

(b) A toy car crashes into a wall and rebounds at right angles to the wall, as shown in the plan view.

The graph shows the variation with time of the force acting on the car due to the wall during the collision.

65
The kinetic energy of the car is unchanged after the collision. The mass of the car is 0.80 kg.
(i) Determine the initial momentum of the car. [3]

………………………………………………………………………………………………………………

(ii) Estimate the average acceleration of the car before it rebounds. [3]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(iii) On the axes, draw a graph to show how the momentum of the car varies during the impact. You are
not required to give values on the y-axis. [3]
66
(c) Two identical toy cars, A and B are dropped from the same height onto a solid floor without rebounding.
Car A is unprotected whilst car B is in a box with protective packaging around the toy. Explain why car
B is less likely to be damaged when dropped. [4]

………………………………………………………………………………………………………………

MAY 2015 – TZ 1 – HL – PAPER 2 – Q. 2

44. This question is about the forces on a skier.

A skier is pulled up a hill by a rope at a steady velocity. The hill makes an angle of 12˚ with the
horizontal. The mass of the skier and skis is 73 kg. The diagram below shows three of the forces
acting on the skier.

67
(a) On the diagram, draw and label one other force acting on the skier. [1]
(b) Calculate the magnitude of the normal reaction acting on the skier. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(c) The total frictional force acting is 65 N. Determine the tension in the rope. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(d) Explain, using Newton’s first law of motion, why the resultant force on the skier must be zero. [2]

………………………………………………………………………………………………………………

November 2015 – TZ 0 – HL – PAPER 2 – Q. 8 (PART 1)

45. This question is about kinematics and Newton’s laws of motion.

Cars I and B are on a straight race track. I is moving at a constant speed of 45 m s–1 and B is initially
at rest. As I passes B, B starts to move with an acceleration of 3.2 m s –2.

At a later time B passes I. You may assume that both cars are point particles.
(a) (i) Show that the time taken for B to pass I is approximately 28 s. [4]

………………………………………………………………………………………………………………

68
………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(ii) Calculate the distance travelled by B in this time. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(b) B slows down while I remains at a constant speed. The driver in each car wears a seat belt. Using
Newton’s laws of motion, explain the difference in the tension in the seat belts of the two cars. [3]

………………………………………………………………………………………………………………

(c) A third car O with mass 930 kg joins the race. O collides with I from behind, moving along the same
straight line as I. Before the collision the speed of I is 45 m s–1 and its mass is 850 kg. After the
collision, I and O stick together and move in a straight line with an initial combined speed of 52 m s –
1
.
(i) Calculate the speed of O immediately before the collision. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(ii) The duration of the collision is 0.45 s. Determine the average force acting on O. [2]

………………………………………………………………………………………………………………

MAY 2016 – TZ 0 – HL – PAPER 2 – Q. 1

69
46. A company designs a spring system for loading ice blocks onto a truck. The ice block is placed in a holder H
in front of the spring and an electric motor compresses the spring by pushing H to the left. When the spring is
released the ice block is accelerated towards a ramp ABC. When the spring is fully decompressed, the ice
block loses contact with the spring at A. The mass of the ice block is 55 kg.

Assume that the surface of the ramp is frictionless and that the masses of the spring and the holder are
negligible compared to the mass of the ice block.
(a) (i) The block arrives at C with a speed of 0.90 m s−1. Show that the elastic energy stored in the spring is 670 J.
[2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(ii) Calculate the speed of the block at A. [2]

………………………………………………………………………………………………………………

(b) Describe the motion of the block

(i) from A to B with reference to Newton's first law. [1]

………………………………………………………………………………………………………………

(ii) from B to C with reference to Newton's second law. [2]

………………………………………………………………………………………………………………

(c) On the axes, sketch a graph to show how the displacement of the block varies with time from A to C. (You do
not have to put numbers on the axes.) [2]

70
(d) The spring decompression takes 0.42 s. Determine the average force that the spring exerts on the block. [2]

………………………………………………………………………………………………………………

(e) The electric motor is connected to a source of potential difference 120 V and draws a current of 6.8 A. The
motor takes 1.5 s to compress the spring. Estimate the efficiency of the motor. [2]

………………………………………………………………………………………………………………

(f) On a particular day, the ice blocks experience a frictional force because the section of the ramp from A to B is
not cleaned properly. The coefficient of dynamic friction between the ice blocks and the ramp AB is 0.030.
The length of AB is 2.0 m.

Determine whether the ice blocks will be able to reach C. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
71
………………………………………………………………………………………………………………

November 2016 – TZ 0 – HL – PAPER 2 – Q. 1

47. A tennis ball is hit with a racket from a point 1.5 m above the floor. The ceiling is 8.0 m above the floor. The
initial velocity of the ball is 15 m s–1 at 50° above the horizontal. Assume that air resistance is negligible.

(a) Determine whether the ball will hit the ceiling. [3]

………………………………………………………………………………………………………………

(b) The tennis ball was stationary before being hit. It has a mass of 5.8×10–2 kg and was in contact with the racket
for 23 ms.

(i) Calculate the mean force exerted by the racket on the ball. [1]

………………………………………………………………………………………………………………

(ii) Explain how Newton’s third law applies when the racket hits the tennis ball. [2]

………………………………………………………………………………………………………………

MAY 2017 – TZ 1 – HL – PAPER 2 – Q. 1

48. The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground.
Point B is 20 m above level ground.

(a) A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential

72
energy transferred to kinetic energy.

(i) From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the
velocity at B is 12 m s-1. [2]

………………………………………………………………………………………………………………

(ii) Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing
their temperature. Distinguish between internal energy and temperature. [2]

………………………………………………………………………………………………………………

(b) (i) The dot on the following diagram represents the skier as she passes point B. Draw and label the vertical
forces acting on the skier. [2]

73
(ii) The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose
contact with the ground at point B. [3]

………………………………………………………………………………………………………………

Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the
frictional force is constant and that air resistance can be neglected. [3]

………………………………………………………………………………………………………………

(d) At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the
safety net with speed 9.6 m s-1.

(i) Calculate the impulse required from the net to stop the skier and state an appropriate unit for your
answer.[2]

………………………………………………………………………………………………………………

(ii) Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier
than a rigid barrier. [2]

………………………………………………………………………………………………………………

74
MAY 2017 – TZ 2 – HL – PAPER 2 – Q. 1

49. A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable
pulled by a motor that exerts a horizontal force on the glider throughout the launch.

(a) The glider reaches its launch speed of 27.0 m s–1 after accelerating for 11.0 s. Assume that the glider moves
horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the
ground. [2]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(b) The glider and pilot have a total mass of 492 kg. During the acceleration the glider is subject to an average
resistive force of 160 N. Determine the average tension in the cable as the glider accelerates. [3]

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………
(c) The cable is pulled by an electric motor. The motor has an overall efficiency of 23 %. Determine the average
power input to the motor. [3]

………………………………………………………………………………………………………………

(d) After takeoff the cable is released and the unpowered glider moves horizontally at constant speed. The wings
of the glider provide a lift force. The diagram shows the lift force acting on the glider and the direction of
75
motion of the glider.

Draw the forces acting on the glider to complete the free-body diagram. The dotted lines show the horizontal
and vertical directions. [2]

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