P8 Forces in

Balance
1

Forces facts Fold page here

1) What is a scalar? 1) A quantity with magnitude (size) but no direction.

2) What is a vector? 2) A quantity with magnitude (size) and direction.
3) What does the direction of an arrow of a 3) The magnitude of the vector.
vector quantity represent?
4) What does the size of the arrow of a vector 4) The direction of the vector.
quantity represent? 5) A force is a push or pull that acts on an object.
5) What is a force? 6) A Newton.
6) What is the unit of a force? 7) A Newton meter.
7) What can we use to measure a force? 8) A contact force is a force that needs to touch to act.
8) What is a contact force? 9) A non-contact force is a force that does not need to
9) What is a non-contact force? touch to act.
10) Give four examples of contact forces. 10) Friction, air resistance, tension and normal reaction.
11) Give three examples of non-contact forces. 11) Gravitational, electrostatic and magnetic.
12) Give some examples of scalars. 12) Energy, mass, distance, time, power, speed.
13) Give some examples of vectors. 13) Velocity, acceleration, force, displacement.
14) What is mass? 14) It is the amount of matter in an object. It is constant
15) What is the equation for weight? for an object everywhere.
16) What is the value for gravitational field 15) W=m×g
strength on Earth? 16) 9.8 N/kg
17) What is a resultant force? 17) A single force that has the same effect as all forces
18) What is work done? acting together.
18) It is an energy transfer. One joule of work is done
19) What is the equation for work done? when a force of one newton causes a displacement of
20) What does work done against frictional one metre.
forces cause? 19) W=F×s
21) What does one newton-metre equal in 20) A rise in temperature of the object.
joules?
22) What is elastic deformation? 21) One newton-metre equals one joule.
23) What is inelastic deformation? 22) When an object is stretched but can still return to its
24) What is the equation for Hooke’s law original size.
25) What type of energy is stored in a stretched 23) When an object is stretch but does not return to its
spring? original size.
26) What is the relationship between the force 24) F = k × e
applied and the extension of an elastic 25) Elastic potential energy.
object. 26) The extension of an elastic object is directly
proportional to the force applied.

Name ______________________________
Class ______________________________
Teacher ______________________________
 Introduction to forces
1 A force is a push or pull; and forces have unit of Newtons. To measure a force
2 we can use a device called a Newton meter.

3 Scalar quantities have size (“magnitude”) only and no direction.

4 An example of a scalar quantity is mass.

5 Scalar quantities can be added up normally

6 Example: 36 kg + 14 Kg = 50 kg

7 Vectors have both size and direction.

Scalar Vector Sort the quantities into the

correct column:

Mass distance acceleration

speed velocity energy time
power force displacement

8 If one vector is at right angles to another then we

9 can use Pythagoras’ theorem to find out the
10 resultant vector (combined effect of more than one
11 vector).

12 c2 = a2 + b 2

13 We can also use scale diagrams to find a resultant vector.

 Task: Complete in exercise book
Basic
1. What is a force?
2. What is the unit of a force?
3. What do we use to measure
forces?
4. What is the definition of a scalar?
Give three examples of scalars.
5. What is the definition of a vector?
Give three examples of vectors.
6. What is the equation for
Pythagoras’ theorem?
7. Draw scale diagrams (1cm = 1N)
to work out the resultant force in
each of the cases to the right.

Medium
8. Describe the difference between distance and displacement.
9. Use Pythagoras’ theorem to calculate the missing lengths of each triangle to the right.

Hard
10. A woman walks 200m east and then 100m south.
a) Find the total distance travelled.
b) Now find the resultant displacement.
11. Dr. Edmunds’ cat Lola runs after a squirrel 40m North and 30m West.
a) What is the distance that Lola has run?
b) What is Lola’s resultant displacement?
12. An aeroplane travels with a speed of 100 m/s North, and a speed of 20 m/s East. What is
the plane’s overall velocity?

Mass, weight and gravity

1 All objects have a force that
2 attracts them towards each other.
3 This force is due to gravity.
1 Even you attract other objects to you because of gravity, but you have too little
2 mass for the force to be very strong.
3 The strength of gravity at the surface of a planet is determined by its mass. g is a
4 measurement of the gravitational field strength
5 The gravitational field strength on the surface of the earth is 9.8 N/kg

6 Weight is the force caused by gravity. The weight of an object can be calculated
7 using the formula:

8 W=mxg

9 Where W is weight (in Newtons)

10 M is mass (in kg)

11 g is gravitational field strength (in N/kg)

12 The mass of an object is the amount of matter it contains.

13 The mass of an object stays the same wherever it is, but its weight can change
14 depending on the gravitational field strength.

15 This happens if the object goes somewhere where gravity is stronger, or

16 weaker, such as the Moon.

17 The Moon has less mass than the Earth, so its gravity is less than the Earth's
18 gravity.

Basic:
Arnie and Markey have been travelling the Solar
System on a mission to find out about weight on
all the planets. They came to Earth and found out
their mass in kilograms (shown in the picture).
Complete the tables for Arnie and Markey and fill in the
missing numbers. Hint – information from elsewhere in the
Medium: For these questions you need to re-arrange the formula. (g = 9.8 N/kg for
questions 1-5).
1) A Formula 1 car weighs 7150N, calculate its mass.
2) A cat weighs 42 N, calculate its mass.
3) A dog weighs 180 N, calculate its mass.
4) An iPad weighs 2.2 N, calculate its mass in.
5) A Boeing 747 aeroplane weighs 1.9 × 106 N, calculate its mass.
6) A man of mass 70 kg is standing on a planet where he weighs 1750 N. Calculate the planet’s
gravitational field strength.
7) The curiosity Rover was sent to search Mars. It has a mass of 900 kg weighs 3400 N while on
Mars. Calculate Mars’ gravitational field strength.
Hard: Rearranging and unit conversion.
8) An iphone has a weight of 1.2N on Earth. Calculate its mass in grams.
9) A bottle of water has a weight of 10N on Earth. Calculate its mass in grams.
10) A car has a weight of 12 kN on Earth. Calculate its mass in kg.
11) A rocket of mass 133,000 kg has a weight of 500 kN on Mars. Calculate the gravitational field
strength on Mars.

The diagram shows a helicopter being used to rescue a person from the sea.
(a) The mass of the rescued person is 72 kg.

gravitational field strength = 9.8 N/kg

Show clearly how you work out your answer. (2)

______________________________________________________________

______________________________________________________________

Weight = _________________________ N

(b) To lift the person up to the helicopter, the electric motor transformed 21 600 joules of
energy usefully.

(i) Use a form of energy from the box to complete the following sentence.

gravitational potential heat sound

The electric motor transforms electrical energy to kinetic energy. The kinetic

energy is then transformed into useful _________________________ energy.

(1)

(ii) It takes 50 seconds for the electric motor to lift the person up to the helicopter.

Show clearly how you work out your answer and give the unit.

Choose the unit from the list below. (3)

coulomb (C) hertz (Hz) watt (W)

______________________________________________________________

______________________________________________________________

Power = _________________________
 Resultant forces
1 The forces acting on any object can be shown using a
2 force diagram. A force diagram uses labelled arrows to
3 show all the forces acting on the object.

4  The direction of each arrow shows the direction of

5 each force.
6  The length of each arrow is proportional to the size
7 of the force.

8 The motion of the object will depend on the resultant

9 force. This is calculated by adding all the forces together, taking their direction
10 into account. When more than one force acts on an object, the forces combine
11 to form a resultant force.

12 To draw resultant force you need to add one force onto the end of the other
13 and draw a line from the start to the finish.

14 Mini task: Draw the resultant force of the force

15 diagram to the right.

16

17

18 We can draw a scale

19 diagram to find value of resultant force.

20 Mini task: In the space below draw a diagram (1 cm

21 = 1N) of the force diagram to the left.
Basic

1. What does the length of an arrow in a force diagram show?

2. What does the direction of an arrow in a force diagram show?
3. A cat has a weight of 35N and is standing still on a table.
a) What direction does the weight of the cat act in?
b) What is the name of the other force acting on the cat?
c) What direction does the force named in b) act in?
d) Give the size of the force named in b).
e) Draw two arrows on the diagram to represent the two forces acting on the cat. Label your arrows with
the name and size of the force they show.
4. In each of the examples to the right, work out the overall force and
say whether the object is accelerating, decelerating or moving at a
constant speed.

Medium

5. Below we see a top view of an airplane being blown off course by

wind in various directions. Draw the resultant speed and direction of
travel for each case. In which case does the airplane travel fastest &

slowest?

Hard

6. If we ignore air resistance, we can assume that the horizontal velocity of an object does not change.
a) Since there is no acceleration in the horizontal direction, how does the horizontal component of velocity
compare for positions A, B and C?
b) What is the value of the vertical
component of velocity at
position B?
c) How does the vertical
component at position C
position with that of position A?
d) Draw the resultant velocities at
positions B and C.
Figure 1 shows a boat floating on the sea. The boat is stationary.

Figure 1

(a) Figure 2 shows part of the free body diagram for the boat.

Complete the free body diagram for the boat.

Figure 2

(2)

(b) Calculate the mass of the boat.

Use the information given in Figure 2.

gravitational field strength = 9.8 N/kg

Give your answer to two significant figures. (4)

___________________________________________________________________

___________________________________________________________________

Mass = _____________________ kg
(c) Figure 3 shows the boat towing a small dinghy.

Figure 3

The tension force in the tow rope causes a horizontal force forwards and a vertical force
upwards on the dinghy.

horizontal force forwards = 150 N

vertical force upwards = 50 N

Draw a vector diagram to determine the magnitude of the tension force in the tow rope
and the direction of the force this causes on the dinghy.

Magnitude of the tension force in the tow rope = _____________________ N

Direction of the force on the dinghy caused

 by the tension force in the tow rope = _______________________

Work done and energy transfer

1 What happens when a rocket is launched into space?

2 When the rocket’s engines are fired, chemical energy in the fuel is
3 transferred to kinetic energy in the rocket. This transfer of energy is
4 called work.

5 work done = energy transferred

6 This means the units for work are the same as the units for energy – joules. For
7 example, if a person does 500 J of work, then 500 J of energy is transferred.

8 Work done can be calculated using the following equation:

9 W=F×s

10 Where W is the work done (in Joules)

11 F is the force applied (in Newtons)

12 s is the distance travelled (in metres)

13 Example question: Mo Farah uses

14 50,000 Joules of energy while running,
15 at a force of 10 N. How far has he run?

16 Step 1: Write the equation. Rearrange

17 if necessary.
18 s=W÷F
19 Step 2: Write down the variables
20 W = 50,000 J
1 F = 10 N
2 Step 3: Calculate the answer
3 s = 50,000 ÷ 10 = 5,000m

Task: Complete in exercise book

Basic:
W=F×s
1. What is work done?
2. Write the equation for work done. Include the units.
3. Rearrange the equation for force and distance.
4. Calculate the work done if:
a) F = 5 N, d = 5 m b) F = 150 N, d = 0.1 m c) F = 0.2 N, d = 200 m
d) F = 2000 N, d = 1.5 m e) F = 800 N, d = 25 m f) F = 150,000 N, d = 0.5 m
5. What is the work done if we apply a 1.2N force and we move 4m in the direction of force?
6. What is the work done if we apply a 7N force and we move 8m in the direction of the force?
7. A car drives with a force of 300,000 N over a distance of 200m. What is the work done by the car?
Medium: Rearranging needed
8. Calculate the distance moved if:
a) W = 20 J, F = 10 N b) W = 150 J, F = 7.5 N c) W = 200,000 J, F = 2 N
d) W = 300 J, F = 0.5 N e) W = 90,000 J, F = 4.5 N f) W = 3,000 J, F = 9 N
9. Calculate the force if:
a) W = 15 J, d = 0.75 m b) W = 450 J, d = 225 m c) W = 9000 J, d = 3000 m
d) W = 5000 J, d = 1250 m e) W = 140 J, d = 35 m f) W = 800 J, d = 0.2 m
10. What distance is moved if we have a 8 N force and the work done is 90 J?
11. What is the distance moved if we have a 70 N force and work done is 8 J?
12. What force is required to move 7 m if the work done is 9 J?
Hard: Rearranging and unit conversion
13. What is the work done when a force of 5kN is applied to a ball To go from kN to N → ⨯ 1000
and it moves 0.8km?
14. What is the work done to a car if a force of 9kN is applied and it
To go from km to m → ⨯ 1000
moves 7km?
15. What force is required if 2.5kJ moves and object 56cm?
16. Dr. Edmunds’ cat Lola accelerates with a force of 220 N along a To go from cm to m → ÷ 100
distance of 80 cm. Calculate the work done.
17. A teacher is late for a lesson and expends 400,000 J of energy sprinting to a lesson. If the distance
covered is 0.2 km, with what force does the teacher sprint?
18. An aeroplane does 1.2 × 108 J of work in flying a distance of 400 km. With what force is the
aeroplane flying?
19. a) The diagram shows an aircraft and the horizontal
forces acting on it as it moves along a runway. The
resultant force on the aircraft is zero.
i) What is meant by the term resultant force?
ii) Describe the movement of the aircraft when
the resultant force is zero.
 b) The aircraft has a take-off mass of 320,000 kg. Each of the 4 engines can produce a force of 240
kN. The aircraft takes a distance of 0.8 km to take off. Calculate the work done by the aircraft in
taking off.

Q1.
The diagram shows an adult and a child pushing a loaded
shopping trolley.

(a) (i) What is the total force on the trolley due to the
adult and child?

__________________________________ (1)

(ii) Which one of the terms in the box means the

same as total force?

Draw a ring around your answer.

answer force mean force resultant force

(1)

(iii) The trolley is pushed at a constant speed for 80 metres.

Calculate the work done to push the trolley 80 metres.

Show clearly how you work out your answer.

______________________________________________________________

______________________________________________________________

Work done = ______________________________

(2)

(b) Complete the following sentences by drawing a ring around the correct word in each of
the boxes.

joule
(i) The unit of work done is the newton .
watt
(1)

heat
(ii) Most of the work done to push the trolley is transformed into light .
sound
(1)
(Total 6 marks)
Q2.
The diagram shows a climber part way up a cliff.

(a) Complete the sentence.

When the climber moves up the cliff, the climber

gains gravitational ______________________ energy.

(1)

(b) The climber weighs 660 N.

(i) Calculate the work the climber must do against

gravity, to climb to the top of the cliff.

______________________________________________________________

______________________________________________________________

Work done = _________________________ J

(2)

(ii) It takes the climber 800 seconds to climb to the top of the cliff.
During this time the energy transferred to the climber equals the work done by the
climber.

Use the equation in the box to calculate the power of the climber during the climb.

Calculate the power of the climber during the climb.

______________________________________________________________

______________________________________________________________

Power = _________________________ W
(2)
(Total 5 marks)
 Hooke’s law

1 Hooke’s law says that the amount a spring stretches is proportional to the
2 amount of force applied to it.

3 F=k×e

4 Where:

5 • F is the applied force (in newtons, N),

6 • e is the extension (in metres, m)

7 • k is the spring constant (in N/m).

8 The spring constant measures how difficult it is to compress or stretch a spring.

9 The larger the spring constant the more difficult is to compress or stretch.

10

11

12

13

14

15 If a
16 material returns to its original size and shape when you remove the forces
17 stretching or deforming it (reversible deformation), we say that the material is
18 demonstrating elastic behaviour.
1 A plastic (or inelastic) material is one that stays deformed after you have taken
2 the force away. If deformation remains (irreversible deformation) after the
3 forces are removed then it is a sign of plastic behaviour.

4 If you apply too big a force a material will lose its elasticity.

Task: Complete in your exercise book

Basic
1. a) What is the equation that links force, spring constant and extension?
b) What are the units of force, spring constant and extension?
2. Calculate the force on a spring if:
a) k = 10 N/m, e = 0.20 m.
b) k = 25 N/m, e = 0.05 m.
c) k = 150 N/m, e = 0.15 m.
3. If the spring constant is 30 N/m and a spring is stretched by 0.3m, how much force has been
applied?
4. If the spring constant is 12.6 N/m and a spring is stretch by 0.25m, how much force has been
applied?
5. What force would be needed to extend a spring with a spring constant k = 10 N/m by an extension
of 0.3 m?

Medium
6. Re-arrange Hooke’s law to give equations for the spring constant k, and the extension e. You will
need to use these equations for the rest of the medium questions.
7. Calculate the spring constant if:
a) F = 150 N, e = 0.075 m.
b) F = 50 N, e = 0.1 m.
8. Calculate the extension if:
a) F = 15 N, k = 150 N/m.
b) F = 45 N, k = 90 N/m.
9. If a 6N weight is hung on a spring, and it extends by 0.2m, what is the spring constant?
10. If the force applied is 4.5 N and the spring constant is 9 N/m, how much will the spring extend by?

Hard
11. A mass of 620 g is hung on a spring of spring constant 31 N/m.
a) Convert 620 g into kg.
b) Using F = m × g, what is the force of the mass acting on To go from g to kg → ÷ 1000
the spring (g = 10 N/kg)?
c) Calculate the extension of the spring.
12. A spring of spring constant 40 N/m starts at a length of 13 cm, and it extends to a length of 21 cm.
a) What is the extension of the spring (in cm)?
b) Convert this extension into metres. To go from cm to m → ÷ 100
c) What is the force on this spring?
13. A spring has a weight of 200g hanging on it, and has a spring constant of 40 N/m. Calculate the
extension of the spring.
 14. A spring has a weight of 500g hanging on it, and is stretched from a length of 5cm to a length of 15
cm. What is the spring constant of the spring?
15. A spring has a weight of 750g hanging on it, and is stretched from a length of 2.5cm to a length of
10 cm. What is the spring constant of the spring?
Stretch: Write some of your own questions and solve them. To make them hard, put extension in
cm/mm or give a mass in grams. Try to make the numbers realistic.

(a) When a force is applied to a spring, the spring extends by 0.12 m.

The spring has a spring constant of 25 N / m.

Calculate the force applied to the spring.

___________________________________________________________________

___________________________________________________________________

Force = ________________________ N

(b) Figure 1 shows a toy glider. To launch the

glider into the air, the rubber band and glider
are pulled back and then the glider is
released.

(i) Use the correct answers from the box to

complete the sentence.

chemical elastic potential kinetic thermal

When the glider is released, the _________________________ energy

stored in the rubber band decreases and the glider gains

_________________________ energy.

(c) Figure 3 shows the vertical forces, A and B, acting on the

glider when it is flying.

(i) What name is given to the force labelled B?

Draw a ring around the correct answer.

drag friction weight

(ii) Which one of the following describes the downward speed of the glider when force
B is greater than force A?

Tick ( ) one box.

 Downward speed increases

Downward speed is constant

Downward speed decreases

Hooke’s law practical

1 Aim: To investigate the relationship
2 between force applied and the
3 extension of a spring.
4 Materials: A spring, a clamp stand,
5 clamps, rulers, 100g masses and mass
6 hanger.

7 Method:

8 1. Hang the spring on a clamp and

9 add a splint so it’s easier to read the length.
10 2. Making sure the splint is horizontal, take a reading on the ruler – this is the
11 length of the unstretched spring (at Weight = 0.0 N)
12 3. Carefully hook the 100g mass hanger onto the bottom of the spring. This
13 weighs 1.0 newton (1.0 N).
14 4. Take a reading of the length of the spring.
15 5. Add further masses. Measure and record the length of the spring each
16 time. Get at least 8 results.
17 6. Calculate the extension i.e. the amount the string has stretched. To
18 calculate this you subtract the length of the unstretched spring from each
19 of your length readings.
20
21 Write your results in the table below:
22

Mass (kg) Force (N) Length (cm) Extension (cm)

Plot a graph of extension (cm) vs Force (N) on the graph paper below.
Stretch: Calculate the weight (in Newtons) of an unknown object:
1) Calculate the gradient of your straight line.
2) Hang the unknown object on the spring, and measure the extension.
3) The weight of the object is equal to your extension divided by your gradient.
4) Check the weight of the object with the measuring scales.
A student carried out an investigation to determine the spring constant of a spring.

The table gives the data obtained by the student.

(a) The student measured the extension for five different forces rather than just measuring
the extension for one force. Suggest why. (1)

___________________________________________________________________

The diagram below shows some of the data obtained by the student.

(b) Complete the diagram above by plotting the missing data from the table above. Draw the
line of best fit. (2)

(c) Write down the equation that links extension, force and spring constant. (1)

___________________________________________________________________

(d) Calculate the spring constant of the spring that the student used.

Give your answer in newtons per metre. (4)

___________________________________________________________________

___________________________________________________________________
 ___________________________________________________________________

___________________________________________________________________

Spring constant = ______________________ N/m

Distance and displacement

1 Distance is a scalar because it gives how far an object moves regardless of
2 direction.

3 Displacement is a vector because it gives how far an object moves from its start
4 position (measured in a straight line from the start point to the finish point)

5 This is Wayde van Niekerk, the 400 m

6 world and Olympic champion. Wayde
7 also holds the 400 m world record at
8 43.03 s.

9 During a race, Wayde travels a distance

10 of 400 m from start to finish.

11 If he runs on an oval track, what will his

12 displacement be?

13 Because he ends up back where he

14 started his displacement is 0 m.

15 Example question:

16 A cat walks along a path from A to B.

17 Calculate:

18 a) The distance travelled.

19 Distance travelled = 100 + 200 + 300= 600 m
20 b) The displacement.
1 This is more complicated:
2 1. Draw a straight line between the start and finish points.
3 2. Draw a triangle showing how far horizontally and vertically the cat has
4 travelled.
5 3. Use Pythagoras to calculate the displacement and give a direction.
2 2 2
6 a + b =c
2 2 2
7 → 200 +400 =c
8 → c=√ 200,000=447 m North West

Basic
1. Distance is how __________ an object has moved.
2. Its value __________ (can/cannot) be zero.
3. It ______________ (depends/doesn’t depend on
direction).
4. Distance is a ______________ (scalar/vector).
5. Displacement is how _____________ an object has
moved from its ____________ position.
6. Its value ______________ (can/cannot) be zero.
7. It _______________ (depends/doesn’t depend) on direction.
8. Displacement is a _____________ (scalar/vector).
Medium
9. A man swims clockwise around a swimming pool and wants to know how far he has travelled at
certain points. Calculate the distance travelled between:
A→C A→F A→G
B→H F→ A H→A

10. If he
swims around the pool 4.5 times, what is the distance that he has
travelled?
Hard: For some you will need to draw a triangle and use Pythagoras. Remember the direction it’s going in
as well.
11. Now find his displacement between the following points:
A→C A→F A→G
B→H F→ A H→A
12. He swims from point A → B → D for a chat with his friend.
a) Calculate the distance (in km) he has swum.
b) Calculate his displacement (in km). To go from m to km → ÷ 1000
13. He completes 3 laps of the pool.
a) Calculate the distance (in km) he has swum.
b) Calculate his displacement (in km).

A train travels from town A to town B.

Figure 1 shows the route taken by the train.

Figure 1 has been drawn to scale.

Figure 1

(a) The distance the train travels between A and B is not the same as the displacement of
the train.

What is the difference between distance and displacement?

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________
(1)

(b) Use Figure 1 to determine the displacement of the train in travelling from A to B.

Show how you obtain your answer.

___________________________________________________________________

___________________________________________________________________
 Displacement = ___________________ km

Direction = _________________________
(2)

(c) There are places on the journey where the train’s velocity changes without changing
speed.

Explain how this can happen. (2)

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________