Work done: transferring energy with a force
In everyday speech "work" means effort. In physics it means something exact: energy transferred when a force moves an object along the direction of that force. Holding a heavy bag still is tiring, but does no physics work at all, because nothing moves.
Work \( W \) is measured in joules (J), \( F \) is the force in newtons (N), and \( d \) is the distance moved in the direction of the force in metres (m). One joule is the work done when 1 N moves something 1 m.
A student pushes a box with a steady force of 40 N across 3 m of floor. How much work is done?
Kinetic and gravitational potential energy
Once energy has been transferred, it has to go somewhere. Two of the most common stores at MYP level are the energy of movement and the energy of height.
Kinetic energy is the energy an object has because it is moving. Note the velocity is squared, so doubling the speed gives four times the kinetic energy.
Gravitational potential energy is the energy an object has because of its height in a gravitational field.
Here \( m \) is mass in kg, \( v \) is speed in m/s, \( h \) is height in m, and \( g \) is the gravitational field strength, about 9.8 N/kg on Earth (many exams round it to 10 N/kg). Both energies come out in joules.
A 0.4 kg ball is thrown so that it moves at 5 m/s. What is its kinetic energy?
Square before you multiply
In \( E_k = \tfrac12 mv^2 \), the squaring applies only to \( v \), not to the mass or the half. Work out \( v^2 \) as its own step, then multiply. Squaring the whole expression is a classic loss of marks.
Conservation of energy
Energy is never made from nothing and never truly destroyed; it only moves between stores. This is the principle of conservation of energy, and it is one of the deepest ideas in all of physics.
- Conservation of energy
- The total energy of a closed system stays constant. Energy can be transferred from one store to another (for example gravitational to kinetic as something falls), but the total before equals the total after.
A falling ball is the classic case. At the top it has plenty of gravitational potential energy and no kinetic energy. As it drops, \( E_p \) falls and \( E_k \) rises by the same amount, so if we ignore air resistance we can simply write \( mgh = \tfrac12 mv^2 \) and solve for the landing speed.
"Lost" energy is just spread out
When a question says energy is "wasted", it has not vanished. It has usually been transferred to the surroundings as heat and sound. It is still counted; it is just no longer useful.
Power and efficiency
Two cranes might lift the same load to the same height, doing the same work, yet one finishes in half the time. That crane is more powerful. Power is the rate of transferring energy, or the rate of doing work.
Power \( P \) is measured in watts (W), \( E \) is the energy transferred in joules, and \( t \) is the time in seconds. One watt is one joule per second.
No machine transfers every joule usefully. Efficiency tells you what fraction of the input energy comes out doing the job you wanted.
A motor is supplied with 500 J of electrical energy and produces 300 J of useful kinetic energy. What is its efficiency?
Sankey diagrams
A Sankey diagram is a picture of where energy goes. The width of each arrow is drawn in proportion to the number of joules it carries. Energy flows in from the left, the useful part carries straight on, and wasted energy branches off, usually downwards as heat.
| Feature of the diagram | What it tells you |
|---|---|
| Width of the input arrow | Total energy supplied |
| Width of the straight-on arrow | Useful energy output |
| Width of the branching arrows | Energy wasted, usually as heat |
| Total width in = total width out | Conservation of energy in a picture |
Because the arrows must be to scale, a Sankey diagram is really conservation of energy drawn out: every joule that enters on the left has to leave on the right. A thin useful arrow beside a fat wasted one is the visual signature of a low-efficiency device, such as an old filament light bulb.
Where this is assessed
Energy calculations reward Criterion A and, when you process experimental readings into an efficiency, Criterion C. Drawing a clear, to-scale Sankey diagram and commenting on wasted energy is strong evidence for Criterion C communication and Criterion D evaluation.
Check yourself
Have a go before revealing each answer.
1. A crane does 6000 J of work in 4 s lifting a load. What is its power output? +
\( P = \dfrac{E}{t} = \dfrac{6000}{4} = \) 1500 W, which is 1.5 kW.
2. A 2 kg book is lifted onto a shelf 1.5 m high. Taking \( g = 10 \) N/kg, how much gravitational potential energy does it gain? +
\( E_p = mgh = 2 \times 10 \times 1.5 = \) 30 J. This equals the work done lifting it, which is a neat check.
3. A lamp takes in 60 J of electrical energy each second and gives out 9 J of light. State its efficiency and what happens to the rest. +
Efficiency \( = \dfrac{9}{60} \times 100\% = \) 15%. The remaining 51 J is transferred to the surroundings as heat (wasted energy), which is why the lamp feels warm.
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