2.2a – Calculating work done
Work is the measure of energy transferred when a force, , moves an object through a distance, . As one energy store empties and another fills, work is done. Work done, , and energy are both measured in joules ().
The SI unit for work done is the joule (abbreviated as J), which is the same as for other measures of energies. This is used when force is measured in newtons and the distance is measured in meters.
When the force is not changing, the word done is usually straightforward to determine. In some examples at KS4 the force will change (for example, as a spring stretches).
Example work done questions
Consider a nurse pushing a patient in a wheelchair along a corridor. The force required to push the patient is .
How much work does the nurse do in pushing the patient along the corridor?
What are the energy stores involved?
This is calculated by:
The energy in the chemical store decreases from start to finish. At the end, because of friction, the thermal store of energy of the system will have increased.
Vertical work done
The patient and wheelchair then go up 10 m in a lift. How much work is done by the lift on the patient/wheelchair?
What are the energy stores involved?
This is calculated by:
In this case the energy store that is decreasing is whatever is powering the electric motor that drives the lift – so that may be the chemical store of gas in a gas-fuelled power station. The energy store increasing is the gravitational store of energy of the patient/wheelchair.
In both cases, we do not need to consider energy changes when the patient is moving, only the clearly defined start and end points.
Why do we use to stand for displacement? It comes from the latin word spatium which means space… as in the space/interval/gap between two different places. Nearly every awarding body uses in the equations for uniformly accelerated motion (such as ), so it may make sense to always use it to avoid confusion later
You could imagine a similar question that includes extra information:
Consider a nurse pushing a patient in a wheelchair along a corridor. The total weight of the patient and wheelchair is . The force required to push the patient is .
How much work does the nurse do in pushing the patient along the corridor?
The answer is unchanged from earlier (), but students then need to remember that to determine the work done by a force requires the magnitude of the force and the distance that they are moving in the direction of the force.
2.2 – Where do the equations come from?