Physics 8.5 - 8.9 - Work and energy changes

Work as energy transfer

Pearson supplies an equation sheet for the 2025–2027 GCSE Combined Science Physics exams. Practise selecting equations, understanding their quantities, converting units and rearranging them. The independent calculations here include the equation support they need.

In physics, work done has a precise meaning. Choose the object or group of objects that forms the system. When a force acts while an object moves in the force's direction, the force transfers energy mechanically. A force acting opposite the movement transfers energy away from that object's mechanical stores.

An object does not "contain work", and a moving object does not "carry force". A force is an interaction that can change motion; work done measures an associated energy transfer.

There must be movement in the direction of the named force. Holding a stationary bag requires an upward force, but the bag does not move, so that force does no mechanical work on the bag. One joule is transferred when a force of 1 N moves an object 1 m in the force direction.

Measuring and calculating work

To measure the work done by a steady pulling force:

1. Zero a newton meter (force meter), attach it to the object and pull in a straight line.
2. Keep the meter aligned with the direction of movement and record the steady force in newtons.
3. Use a metre rule or tape measure to find the distance moved in that same direction, in metres.
4. Multiply the force by the aligned distance.

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Worked example

A trolley is pulled 2.5 m by a steady horizontal force of 18 N. Calculate the work done by the pulling force.

Solution

The force and movement are in the same direction, so the full 2.5 m is used.

$E = F \times d$

$E = 18\,\mathrm{N} \times 2.5\,\mathrm{m} = 45\,\mathrm{N\,m} = 45\,\mathrm{J}$

The unit product is $1\,\mathrm{N\,m}=1\,\mathrm{J}$, so $45\,\mathrm{N\,m}$ and $45\,\mathrm{J}$ describe the same work. Convert centimetres to metres before multiplying: $250\,\mathrm{cm}=2.50\,\mathrm{m}$. The answer is sensible: each metre transfers 18 J, so 2.5 m transfers more than 36 J but less than 54 J.

Work and energy changes

Work links a force to a change in an energy store. The force is the interaction that changes the system; the work done is the amount of energy transferred.

• When a lifting force raises an object, the gravitational potential energy of the object-Earth system increases.
• When a resultant force speeds up an object, the object's kinetic energy increases.
• When the resultant force opposes the motion, the object's kinetic store decreases. An individual resistive force can do work while another force supplies energy: at constant speed their effects balance, so kinetic energy need not change.

If no other energy transfer needs to be included, the magnitude of the change in the relevant energy store equals the work done:

$\text{change in energy store} = \text{work done}$

Worked example

A resultant force does 85 J of work on a cart on a level track. The cart initially has 25 J of kinetic energy. The force acts in the direction of travel. Calculate its final kinetic energy.

Solution

The force speeds up the cart, so its kinetic store increases by 85 J.