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2133001
Jenny does an experiment to study torque. She applies a force F on different
positions on a door as shown below. O is the hinge. Suppose every time the door
moves with the same speed and the force F is perpendicular to the door.
F
The data obtained is shown in the table below.
Position
F/N
20
23
27
32
41
Distance from O / cm
80
70
60
50
40
(a) When F is applied at A, what is the torque produced?
(2 marks)
(b) Calculate the torque produced by F at the other four positions. What do you
find about their values?
(5 marks)
(c) Explain what you find in (b).
(1 mark)
(d) If F is parallel to AO, can the door be opened? Explain briefly.
(2 marks)
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2133002
An object slides down from a slope to the ground. It keeps moving a distance
before it stops.
(a) Explain why the object does not stop at once when it reaches the ground but
keeps moving for a distance.
(3 marks)
(b) Suggest two methods to make the object stop in a shorter time.
(2 marks)
(c) The horizontal speed of the object is 6 m s1 when it reaches the ground.
The distance it goes before stopping is 12 m. The mass of the object is 2 kg.
()
Find the friction between the object and the ground.
(3 marks)
() A pulling force can be applied to the object so that the distance it goes
before stopping will be halved. How large should the force be?
(2 marks)
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1
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2133003
Jimmys dad drives him home. At a turning, his dad turns the steering wheel
clockwise with both hands.
(a) Draw the forces that Jimmys dad exerts on the steering wheel in the figure
below.
(2 marks)
(b) Jimmy sees his dad turns the steering wheel easily, so he thinks the steering
wheel does not apply force on his dad. Is Jimmy correct? Explain briefly.
(2 marks)
(c) If the force applied on the steering wheel by each hand is 10 N, and the
radius of the steering wheel is 15 cm, find the couple formed.
(2 marks)
(d) Jimmy thinks that when his dad turns the steering wheel, there is a net force
acting on it. Is Jimmy correct? Explain briefly.
(2 marks)
(e) A lot of daily-life tools make use of couple. List three of them.
(3 marks)
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2133004
Darren pushes an object S up to a truck on an inclined board as shown below.
The mass of object S is 50 kg. The length of the board AC = 3 m. S is at rest at
point A. Darren pushes the object S to point B with a force of 400 N in 1 s. The
speed of the object stays constant when it travels from B to C.
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C
B
S
30
(a) Suppose the board is smooth.
()
Draw the free-body diagram of S.
(3 marks)
() Find the length of AB.
(4 marks)
() What is the total time needed to push S from A to C?
(3 marks)
(b) Suppose the friction between the board and the object is 80 N.
()
Find the length of AB.
() What is the total time needed to push S from A to C?
(2 marks)
(3 marks)
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2133005
A student wants to find out how the terminal velocity of a parachute is affected
by its area and mass. She studies with parachutes made from plastic sheets and a
small mass. She mounts a motion sensor from a height with its face down and
drops 3 parachutes of different areas and masses from the motion sensor. Figures
a, b and c show the velocity-time graphs obtained by the motion sensor.
Figure a v-t graph of parachute (area = 30 cm 30 cm, mass = 2.5 g)
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Figure b v-t graph of parachute (area = 30 cm 30 cm, mass = 5.0 g)
Figure c v-t graph of parachute (area = 50 cm 50 cm, mass = 2.5 g)
(a) What are the forces acting on the parachute as it falls? How do these forces
affect the motion of the parachute throughout the fall?
(5 marks)
(b) Suggest a reason why the v-t graphs are not smooth.
(1 mark)
(c) From the v-t graphs, what are the terminal velocities of the parachutes?
(3 marks)
(d) Comparing the graphs, suggest how the terminal velocity is affected by
(i)
the mass,
(ii) the area of the parachute.
State whether the terminal velocity increases or decreases with the change
of mass and area.
(2 marks)
(e) Explain the findings in (d) in terms of the forces acting on the parachute.
(4 marks)
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2133006
(a) A block of mass 5 kg is placed on a rough surface as shown in Figure a. A
horizontal force F of 5 N is applied on it. The block moves at a constant
velocity of 1 m s1.
5 kg
F
rough surface
Figure a
(i)
Find the friction between the block and the table.
(1 mark)
(ii) Calculate the acceleration of the block if F is increased to 10 N.
(2 marks)
(b) The 5-kg block and another 10-kg block are then placed together on a
smooth surface as shown in Figure b. A 75-N force is applied horizontally
towards the right against the 5-kg block.
75 N
10 kg
5 kg
smooth surface
Figure b
(i)
(1) Calculate the net force acting on the 5-kg block.
(2) Calculate the net force acting on the 10-kg block by the 5-kg
block.
(3 marks)
(ii) A student says that the force acting on the 5-kg block by the 10-kg
block is the same as that in part (b)(i)(2). Without doing any
calculation, comment on this statement.
(3 marks)
(c) The blocks are then rearranged as shown in Figure c.
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10 kg
smooth surface
5 kg
Figure c
(i)
Calculate the acceleration of the blocks.
(3 marks)
(ii) A student says that if the 5-kg block is replaced by a pulling force of
50 N vertically downwards, the acceleration of the 10-kg block will be
the same as in (c)(i). Comment on this statement.
(3 marks)
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2133007
In Figure a, a girl of mass 60 kg is standing on a weighing scale in a lift of mass
740 kg.
Figure a
Figure b shows the velocity-time graph of the lift.
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velocity / m s1
20
25
time / s
Figure b
The mass of the weighing scale can be neglected. Take the upward direction as
positive.
(a) Find the acceleration of the lift from
(i)
05 s,
(ii) 520 s,
(iii) 2025 s.
Hence sketch the acceleration-time graph of the lift.
(5 marks)
(b) If the breaking tension of the cable of the lift is 24 000 N, calculate the
maximum possible acceleration of the lift with the girl.
(2 marks)
(c) (i)
Find the weight of the girl.
(1 mark)
(ii) What is the reading of the weighing scale during
(1) 0 to 5 s,
(2) 5 to 20 s,
(3) 20 to 25 s?
(3 marks)
(d)
If the cable of the lift breaks, the lift undergoes free falling. The reading of
the weighing scale becomes zero. A student states that the weight of the
girl becomes zero. Comment on the students statement.
(3 marks)
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2133008
The figure below shows a mass suspended by a light inextensible string. A spring
balance is attached to the mass and pulled horizontally so that the string is
inclined at an angle with the horizontal.
7
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(a) Draw a labelled diagram to show all the forces acting on the mass.
(3 marks)
(b) What is the resultant force on the mass?
(1 mark)
(c) A student performs an experiment to find the relationship between F and .
Different values of are used and the corresponding values of F are
measured. The results obtained are shown below:
(i)
50
45
40
35
30
F/N
8.0
10.0
12.0
14.5
17.0
Using a scale of 1 cm representing 2 N (y-axis) and 1 cm representing
0.2 (x-axis), plot a graph of F (y-axis) against
1
tan
(x-axis).
(5 marks)
(ii) Find the slope of the graph.
(2 marks)
(iii) State the physical meaning of the slope of the graph.
(2 marks)
(iv) Find the tension in the string when = 45.
(2 marks)
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2133009
The figure below shows a block of mass 4 kg placed on a rough plane inclined at
30 to the horizontal. The block is pushed up the plane by a 45-N force acting
parallel to the plane. The block moves with uniform velocity.
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45 N
30
(a) Draw a labelled diagram to show all the forces acting on the block.
(3
marks)
(b) Find the normal reaction acting on the block by the plane.
(3 marks)
(c) Find the friction between the block and the plane.
(3 marks)
(d) If the 45 N force is removed suddenly, describe fully the subsequent motion
of the block. Explain briefly.
(4 marks)
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2133010
An object of mass 1 kg is hung by a spring balance inside a box. The following
figure shows the whole set-up that is placed on the ground. It is known that the
mass of the set-up is 5 kg.
The box is then dropped from a height to the ground.
(a) What is the weight of the object?
(1 mark)
(b) If air resistance is ignored, what is the acceleration of the box as it falls?
(1 mark)
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(c) If air resistance should be taken into consideration, how will it affect the
acceleration of the box? Explain briefly.
(2 marks)
(d) It is found that the box finally falls with a constant speed.
(i)
Explain why this happens.
(3 marks)
(ii) What is the air resistance when this happens?
(1 mark)
(e) What is the reading of the spring balance when
(i)
the box accelerates at g?
(ii) the box attains a constant speed?
Explain your answers briefly.
(3 marks)
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2133011
Two blocks on a smooth ground are connected together with a string. A force of
50 N pulls the blocks to the right.
string
A
5 kg
50 N
3 kg
(a) Draw the free-body diagram for block A.
(3 marks)
(b) Draw the free-body diagram for block B.
(4 marks)
(c) Find the tension in the string?
(3 marks)
(d) Block A is put on a rough plane inclined at 30 to the horizontal. A force F
parallel to the plane acts on the block.
F
A
30
When F = 35 N, the block starts to move. Find the friction between the
block and the plane.
(2 marks)
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