How Does Work Link Forces To Energy Transfer
Work
Results from the application of force over distance. When work is
done, energy is transformed from one form to another.
- In physics, work is not the same as effort or tiredness.
- Work describes how energy is transferred when a force causes an object to move.
- Work is only done when a force causes movement in the direction of that force.
- If there is no movement, no work is done, even if a force is applied.
Calculating Work Done
- The amount of work done depends on how large the force is.
- It also depends on how far the object moves.
- The distance considered is only the distance moved in the direction of the force.
$$W = Fd$$
where:
- $W$ is work (joules, J)
- $F$ is force (newtons, N)
- $d$ is distance moved (metres, m)
Work is measured in joules (J).
When Work Is Done
- Work is done when a force causes movement in the same direction as the force.
- Work is also done when movement is opposite to the force, such as lifting against gravity.
- In these cases, energy is transferred into or out of the object.
Lifting a bag onto a shelf transfers energy from your muscles to the bag.
When Work Is NOT Done
- No work is done if an object does not move.
- No work is done if the motion is at right angles to the force.
- Even strong forces may transfer no energy if they do not cause movement.
- Think “WORK = MOVE”.
- If there is no movement in the force’s direction, your brain should immediately think “no work”.
Pushing sideways on a wall does not transfer energy because the wall does not move.
Thinking that holding a heavy object still means work is being done in physics.
Positive And Negative Work
- Positive work: the force adds energy to the object (speed increases).
- Negative work: the force removes energy from the object (speed decreases), for example friction or braking.
Do machines reduce the amount of work needed?
- Machines make tasks easier by changing how forces are applied.
- They allow a smaller force to be used over a longer distance.
- Machines do not reduce the total work done.
- They change how the work is carried out.
Using a ramp makes lifting a heavy object easier, but the distance moved increases.
Power Tells You How Fast Energy Is Transferred
Power
Power is the rate at which energy is transferred or work is done.
- Sometimes the key question is not only "How much energy?" but also "How quickly?"
- Power describes how quickly energy is transferred.
- Two systems may transfer the same energy but at different speeds.
- The system that transfers energy faster has greater power.
Calculating power
The defining equation is
$$P = \frac{E}{t}$$
where:
- $P$ is power (watts, W)
- $E$ is energy transferred (joules, J)
- $t$ is time taken (seconds, s)
Since $1\ \text{W} = 1\ \text{J s}^{-1}$, a device rated at 1000 W transfers 1000 J of energy every second.
Connecting Work And Power In Mechanical Situations
If the energy transfer is mechanical work, then
$$P = \frac{W}{t}$$
A useful rearrangement for constant speed motion is:
$$P = Fv$$
because if $W = Fd$ and $d = vt$, then $P = \frac{Fd}{t} = Fv$.
When you are given a "doing something faster" situation (running upstairs quickly, lifting rapidly, accelerating hard), power is often the target quantity.
An 80 kg person runs up a flight of stairs with a vertical height of 12 m in 5 s.
a) Calculate the energy transferred by the person.
b) Calculate the person’s average power output.
Solution
Working (guided):
- Energy transferred is the work done against gravity.
- The person’s weight provides the force.
- The vertical height is the distance.
Energy transferred:
$$ E = mgh = 80 \times 9.8 \times 12 \approx 9.4 \times 10^3 \text{ J}$$
Average power:
$$P = \frac{E}{t} = \frac{9400}{5} \approx 1900 \text{ W}$$
So the person’s average power output is about 1900 W.
Why Is Not all Input Energy Useful?
Efficiency
Using scarce resources in the best possible way to avoid welfare loss.
- Real processes never convert all input energy into the desired output.
- Some energy is always transferred into other forms, very often thermal energy due to friction or electrical resistance.
Calculating efficiency
Using energy:
$$\text{efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}\times 100\%$$
Using power:
$$\text{efficiency} = \frac{\text{useful output power}}{\text{total input power}}\times 100\%$$
These are equivalent when the input and output are measured over the same time interval.
- If you calculate an efficiency greater than 100%, do not just write it down.
- Efficiency above 100% violates conservation of energy, so you must check assumptions, units (kJ vs J), and what counts as "input".
A lift is used to raise a mass of 800 kg through a vertical height of 10 m.
The energy supplied to the lift is 47 kJ.
a) Calculate the useful output energy.
b) Calculate the efficiency of the lift.
Solution
Useful output energy:
$$E_\text{useful} = mgh = 800 \times 9.8 \times 10 = 78\,400 \text{ J}$$
Efficiency:
$$\eta = \frac{78\,400}{47\,000} \times 100\% \approx 167\%$$
Why Wasted Energy Is Often Thermal
- In mechanical systems, friction converts kinetic energy into microscopic motion of particles, increasing temperature.
- In electrical systems, resistance causes heating in wires and components.
- This "wasted" energy is still conserved, but it is usually less useful because it spreads into the surroundings.
- Efficiency is like paying for a full pizza (input), but only a slice ends up on your plate (useful output) because the rest is shared around the table (wasted output).
- You did not lose pizza, but you did not get all of it for your purpose.
A filament bulb might be about 5% efficient for visible light output.
If it takes 60 W electrical input, then useful light power is approximately:
$$P_\text{useful} = 0.05\times 60 = 3\ \text{W}$$
Wasted thermal power is:
$$P_\text{wasted} = 60 - 3 = 57\ \text{W}$$
1. Identify whether the question is about energy/work, power, or efficiency (sometimes all three).
2. Write the relevant relationship first: $W=Fd$, $P=E/t$, $P=VI$, or $\eta=\text{useful}/\text{total}$.
3. Track units carefully: J, W, s, N, m, V, A. Convert kJ to J when needed.
4. For efficiency, state clearly what counts as "useful output" in the context.
5. Do a reasonableness check: efficiencies must be between 0% and 100%, and higher efficiency should mean less wasted energy.
- Explain why work is only done when movement occurs.
- Describe a situation where work is done against gravity.
- Explain why machines do not reduce the total work done.
- Distinguish clearly between energy and power.
- Explain why efficiencies above 100% are impossible.
- Identify one source of energy loss in a household device.
