When a FORCE causes an object to move through a DISTANCE, WORK IS DONE.
Work is an energy transfer — doing work transfers energy from one store to another.
EQUATION:
W = F × s
W = work done (joules, J)
F = force (newtons, N)
s = distance moved along the line of action of the force (metres, m)
1 joule = 1 newton-metre (1 J = 1 N·m).
KEY CONDITION:
Work is only done when the object moves IN THE DIRECTION the force acts.
If the force and motion are at right angles → no work done by that force.
Example: carrying a heavy bag horizontally — the vertical weight does no work (no vertical movement).
Work and Energy
Work done = energy transferred.
ENERGY TRANSFERS THROUGH WORK:
Pushing a box along the floor: work done against friction → kinetic energy of box + thermal energy (friction).
Lifting an object: work done against gravity → gravitational PE gained.
Compressing a spring: work done by force → elastic PE stored.
Braking a car: friction does work → kinetic energy → thermal energy.
EXAMPLE 1:
A 500 N force pushes a box 4 m along the floor.
W = 500 × 4 = 2000 J of energy transferred.
EXAMPLE 2:
How far does a 200 N force push an object if 1000 J of work is done?
s = W ÷ F = 1000 ÷ 200 = 5 m
LINK TO POWER:
P = W ÷ t = F × s ÷ t = F × v
Power also equals force × speed (for constant force and velocity).
Joules and Newtons
UNIT CHECK — understanding dimensions:
1 J = 1 N × 1 m = 1 N·m
This is why energy and work have the same units (joules).
COMMON CONTEXTS:
Lifting: W = F × h (where F = weight = mg and h = height)
Combined with W = mg: W = mgh — same as GPE equation.
EXAMPLE — lifting:
Lift 5 kg by 2 m:
Force needed = weight = 5 × 9.8 = 49 N
Work done = 49 × 2 = 98 J
This equals the GPE gained (Ep = mgh = 5 × 9.8 × 2 = 98 J) ✓
FRICTION AND WORK:
Friction always acts OPPOSITE to motion — it always does NEGATIVE work on moving objects (takes energy from kinetic store → thermal store).
This is why machines that involve friction always need a continuous energy input to keep moving.
⚠️ Common Mistake
Work is only done when the object moves IN THE DIRECTION of the force. Holding a heavy weight stationary does NO work (no displacement) — even though it feels tiring. Also: W in this equation is work done (joules), NOT weight.
📐 Variables
WWork done (W) is measured in joules (J)
FForce (F) is measured in newtons (N)
sDistance moved in direction of force (s) is measured in metres (m)
📐 Key Equations
W = F × s
📌 Key Note
W = Fs. Work done = energy transferred (J). 1 J = 1 N × 1 m. Work only done if object moves in force direction. Lifting = GPE gained = mgh = Fs. Friction does work → thermal energy. P = Fv (force × speed for constant motion).
🎯 Matching Activity — Work Done Calculations
Match each scenario to the correct work done value. — drag the symbols on the right to match the component names on the left.
2000 J
Drop here
98 J
Drop here
0 J
Drop here
5 m
Drop here
Lifting 5 kg by 2 m — W = mgh = 5 × 9.8 × 2
1000 J work done by a 200 N force — s = W ÷ F = 1000 ÷ 200
500 N force moves object 4 m — W = 500 × 4
Holding a 100 N weight stationary — no displacement, no work done
⚽ FIFA Worked Examples
Work Done
A 300 N force moves a crate 6 m along a floor. Calculate the work done.
F
W = F × s
I
F = 300 N, s = 6 m
F
W = 300 × 6
A
W = 1800 J
🎯 Test Yourself
Question 1 of 2
1. A person carries a 20 kg box horizontally for 10 m at constant height. How much work does gravity do on the box?
2. A 400 N force does 3200 J of work. How far does the object move?
⭐ How Well Do You Understand This Topic?
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