Work Done and Energy Transfer

This lesson covers work done and its relationship to energy transfer, using the equation $W = Fd$W=Fd, as required by the Edexcel GCSE Combined Science specification (1SC0). Work done is one of the most frequently examined calculations in the physics papers.

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What Is Work Done?

Work is done when a force causes an object to move. The amount of work done equals the amount of energy transferred.

$W = Fd$W=Fd

where:

• W = work done in joules (J)
• F = force in newtons (N)
• d = distance moved in the direction of the force in metres (m)

Quantity	Unit	Symbol
Work done	joule	J
Force	newton	N
Distance	metre	m

Key Points

• 1 joule of work is done when a force of 1 N moves an object 1 m in the direction of the force.
• Work done = energy transferred. They are the same quantity, measured in joules.
• If the force and the direction of movement are not in the same direction, you only use the component of the force in the direction of movement.

Exam Tip: The equation W = Fd is one of the most important in physics. Remember that d is the distance moved in the direction of the force, not just any distance. If an object moves at right angles to the force, no work is done by that force.

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Worked Examples

Worked Example 1

A person pushes a box with a force of 50 N across a floor for 8 m. Calculate the work done.

1. Write the equation: $W = Fd$W=Fd
2. Substitute: $W = 50 \times 8$W=50×8
3. $W = 400 \text{ J}$W=400 J
4. Answer: W = 400 J

Worked Example 2

A crane lifts a 200 kg crate to a height of 15 m. Calculate the work done. (g = 9.8 N/kg)

1. First find the weight (force): $F = mg = 200 \times 9.8 = 1960 \text{ N}$F=mg=200×9.8=1960 N
2. $W = Fd = 1960 \times 15 = 29\,400 \text{ J}$W=Fd=1960×15=29400 J
3. Answer: W = 29 400 J (or 29.4 kJ)

Note: This work done equals the GPE gained — showing the link between W = Fd and GPE = mgh.

Worked Example 3

A braking force of 4000 N brings a car to rest over 25 m. How much energy is transferred to the thermal store of the brakes?

1. $W = Fd = 4000 \times 25 = 100\,000 \text{ J}$W=Fd=4000×25=100000 J
2. Answer: 100 000 J (100 kJ) is transferred to the thermal store.

Exam Tip: When a braking force is used, the work done by the brakes equals the kinetic energy lost by the vehicle. This links W = Fd with KE = ½mv².

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Work Done Against Friction

When you push an object along a rough surface, the friction force opposes the motion. The work done against friction is transferred to the thermal store of the surfaces and the surroundings.

flowchart LR
    A["Chemical store\n(person)"] -->|Mechanically| B["Kinetic store\n(box)"]
    B -->|By heating\n(friction)| C["Thermal store\n(floor & box)"]

Worked Example 4

A child drags a 10 kg sled across snow for 30 m. The friction force is 15 N. Calculate the work done against friction.

1. $W = Fd = 15 \times 30 = 450 \text{ J}$W=Fd=15×30=450 J
2. Answer: 450 J is transferred to the thermal store of the snow and sled.

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Work Done and Gravity

When lifting an object, you do work against gravity. The energy is transferred to the gravitational potential store.

$W = Fd = mg \times h = mgh = GPE$W=Fd=mg×h=mgh=GPE

This shows that the work done equation and the GPE equation are the same when the force is gravity and the distance is the height.

Worked Example 5

A weightlifter raises a 60 kg barbell by 2 m. Calculate the work done. (g = 10 N/kg)

1. $F = mg = 60 \times 10 = 600 \text{ N}$F=mg=60×10=600 N
2. $W = Fd = 600 \times 2 = 1200 \text{ J}$W=Fd=600×2=1200 J
3. Answer: W = 1200 J

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When Is No Work Done?

No work is done when:

• The object does not move (d = 0).
• The force is perpendicular to the direction of motion (e.g., the normal contact force on a ball rolling on a flat surface).
• There is no force acting (F = 0).

Scenario	Work done?	Reason
Holding a heavy bag still	No	d = 0 — no movement
Pushing a wall that doesn't move	No	d = 0
Satellite orbiting (gravity perpendicular to motion)	No (by gravity)	Force perpendicular to motion
Kicking a ball	Yes	Force causes movement

Exam Tip: A common exam question asks why no work is done when you hold a heavy object still. The answer is that the object does not move, so d = 0 and therefore W = Fd = 0.

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Rearranging the Equation

To find	Rearranged equation
W	$W = Fd$W=Fd
F	$F = \frac{W}{d}$F=dW​
d	$d = \frac{W}{F}$d=FW​

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Summary

• Work done is the energy transferred when a force moves an object: $W = Fd$W=Fd.
• Work done and energy transferred are the same thing, both measured in joules.
• The distance must be in the direction of the force.
• Work done against friction is transferred to the thermal store.
• Work done against gravity equals the GPE gained: $W = Fd = mgh$W=Fd=mgh.
• No work is done if there is no movement, or if the force is perpendicular to the motion.

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Extended Worked Examples

Worked Example 6 — Pushing a Supermarket Trolley

A shopper applies a 40 N horizontal force to push a trolley 12 m across a level floor. Friction opposes motion with a force of 10 N.