Energy Transfer and Work
In 2021, Australian Paralympic rower Nikki Ayers applied 300 N over 6 metres per stroke, and every joule went straight into the boat's motion.
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Q1 · You hold a heavy schoolbag still at arm's length for 30 seconds. Your arm gets tired and warm. Do you think you have done any scientific "work" on the bag? What do you think "work" means in science?
Q2 · A powerful car and a small car both push the same object the same distance along flat ground. Does the powerful car do more work? Why might power and work be different things?
Key Relationships, This Lesson
● Know
- The definition of work in physics: force × distance
- The definition of power: work ÷ time
- The units: joules (J) for work, watts (W) for power
● Understand
- Why work is a measure of energy transfer
- Why power depends on both work and time
- The difference between doing more work and working more powerfully
● Can do
- Calculate work done when force and distance are known
- Calculate power when work and time are known
- Use work and power to compare human and machine performance
Wrong: "If I hold a heavy box still, I am doing work because I am using effort."
Right: In science, work is only done when a force moves an object in the direction of that force. If the box doesn't move, no work is done on it, regardless of how much effort it takes.
Wrong: In physics, work is only done when the object moves in the direction of the force. Holding a box still requires muscle effort, but no work is done on the box because the distance moved is zero. Your muscles are converting chemical energy into thermal energy (you get tired and warm), but zero work is done on the box.
Right: Your muscles do convert chemical energy to heat while you hold the box (which is why you tire and warm up), but zero scientific work is done on the box itself because it doesn't move. Effort and scientific work are not the same thing.
Wrong: "A more powerful machine always does more work than a less powerful one."
Right: Power measures how fast work is done, not how much total work is done. A more powerful machine does the same work in less time, it doesn't necessarily do more work overall.
Wrong: Power measures how fast work is done, not how much work is done. A 2,000 W kettle boils water faster than a 1,000 W kettle, but both do the same amount of work (transfer the same energy) to boil the same amount of water. The 2,000 W kettle just does it in half the time.
Right: Power (watts) and work (joules) measure different things. Two machines can do identical amounts of work, the more powerful one just finishes faster. Always ask "how much work?" separately from "how fast?"
Work and Power in Action
Push a heavy desk across the classroom floor, you feel the strain, the desk slides 2 metres, and you end up panting. Now stand and just hold that same desk off the ground for the same time, equally exhausting, yet the desk goes nowhere. Science says you did work in the first case and zero work in the second. In physics, work has a precise meaning: work is done when a force causes an object to move in the direction of the force. The formula is: W = F × d, where W is work in joules, F is force in newtons, and d is distance in metres.
This definition catches many students off guard. If you hold a heavy backpack at arm's length, your muscles are straining and you feel tired, but you are doing zero work on the backpack because it is not moving. The energy your body burns is actually going into heat inside your muscles, not into moving the pack.
Pushing a box 3 metres across the floor with a force of 50 N does W = 50 × 3 = 150 J of work. Pushing with the same force against a wall that does not move does zero work, no matter how hard you push or how tired you get.
Students often equate effort with work. In everyday language, holding something heavy feels like work. In physics, work requires displacement in the direction of the force. Without movement, no work is done on the object, even though your body is certainly expending chemical energy and producing heat.
Work and energy are intimately linked. When you do work on an object, you transfer energy to it. Lifting a box increases its gravitational potential energy by exactly the amount of work you did: W = mgh. Pushing a box across a rough floor transfers energy to thermal energy in the floor and box via friction.
The direction matters. If you carry a box horizontally, the upward force you apply does no work because the displacement is sideways, perpendicular to the force. Gravity also does no work during horizontal motion because gravity acts vertically. Only the force component in the direction of motion contributes to work.
A hiker climbing a 500 m mountain gains gravitational potential energy equal to the work done against gravity. Whether they take a steep direct path or a gentle zig-zag trail, the total work is the same: mgh. The zig-zag reduces the force needed at any moment but increases the distance.
Two students carry identical boxes up identical stairs. Student A walks straight up. Student B walks up a longer ramp to the same height. Who does more work against gravity?
Both students do exactly the same work against gravity: W = mgh. The ramp is longer but requires less force. The product of force and distance stays constant. Student B takes more time and travels farther, but the work done is identical.
Use these terms in your explanation: force · distance · work · gravitational potential energy
Power is the rate at which work is done or energy is transferred. It is calculated as P = W ÷ twork divided by time. A powerful engine does the same work as a weak one, but faster. Power is measured in watts (W), where one watt equals one joule per second.
This distinction between work and power is crucial. A small electric motor might lift a load slowly using little power. A large motor lifts the same load quickly using more power. The work is identical; the power differs because of the time taken.
A 60 W light bulb converts 60 joules of electrical energy into light and heat every second. A 100 W bulb does the same job faster, more energy per second, which is why it is brighter.
The AEMO (Australian Energy Market Operator) manages power across the national grid, ensuring that electricity generation matches demand every second. A power station's output is measured in megawatts (MW), millions of joules per second.
Calculate work done and power output
Copy Into Your Books
▼Work
- W = F × d
- Unit: joules (J)
- Work = force × distance (same direction)
- No movement = no work done
- Work is energy transfer
Power
- P = W ÷ t
- P = E ÷ t
- Unit: watts (W)
- Power = rate of work/energy transfer
- Higher power = faster work
Australian Power Outputs
- Human brain: ~20 W
- Human walking: ~250 W
- Pro cyclist: ~400 W
- AFL midfielder peak: ~1,000 W
- Family car: ~75 kW
- Tesla battery: ~150 MW
- Loy Yang coal: ~2.2 GW
Exam Tips
- Always state the formula first
- Substitute values with units
- Give final answer with units
- Check force and distance directions match
- Convert time to seconds for power
Work and Power Calculations
1 A miner pushes a loaded cart with a horizontal force of 200 N for 15 metres along a tunnel. Calculate the work done.
2 A student climbs a rope in a gym, lifting their 55 kg body 4 metres off the ground. Calculate the work done against gravity. (Use F = m × g, where g = 10 N/kg.)
3 A crane lifts a 2,000 kg steel beam 12 metres in 8 seconds. Calculate the work done and the power output of the crane. (Use g = 10 N/kg.)
4 A 60 W light bulb is left on for 5 hours. Calculate the total electrical energy transferred. Give your answer in both joules and kilowatt-hours.
Comparing Human and Machine Power
At the start of this lesson you were puzzled by the schoolbag scenario: holding a heavy bag still for 30 seconds makes your arm burn, yet science says you've done zero work. Now that you understand force × distance, does that make sense?
Write a clear explanation of why "holding still" doesn't count as work in physics, and where the burning energy in your arm really goes.
Q1. 6. A Sydney Tower Eye elevator lifts a total mass of 1,200 kg (passengers plus cabin) from ground level to the observation deck 250 metres above. Calculate the work done by the elevator motor. If the lift takes 45 seconds, calculate the power output. (Use g = 10 N/kg.)
1 mark for correct force calculation. 1 mark for correct work. 1 mark for correct power.Q2. 7. A family is choosing between two air conditioners for their home in Darwin. Unit A has a cooling power of 2,500 W and costs $800. Unit B has a cooling power of 5,000 W and costs $1,200. Both units run on electricity that costs $0.30 per kWh. The family needs to remove 18,000 kJ of thermal energy from their house each hour on a hot day.
1 mark for calculating time for each unit to remove 18,000 kJ. 1 mark for calculating energy used by each unit in one hour. 1 mark for explaining that Unit B removes heat faster but uses more electricity per hour. 1 mark for a justified recommendation considering Darwin's climate (long hot season makes operating cost significant).Q3. 8. A mining company claims their new electric haul truck is "better than diesel because it has a more powerful motor." The diesel truck has a 2,500 kW engine at 35% efficiency. The electric truck has a 2,000 kW motor at 85% efficiency. Both trucks do the same 200 MJ of useful work climbing a ramp.
1 mark for calculating diesel energy input (≈571 MJ). 1 mark for calculating electric energy input (≈235 MJ). 1 mark for calculating time for each truck (diesel 80 s, electric 100 s). 1 mark for explaining that the electric truck uses less than half the energy despite being less powerful. 1 mark for a balanced conclusion about what "better" means in this context.Model answers (click to reveal)
Comprehensive Answers
▼Activity 1, Work and Power Calculations
1. Miner pushing cart: W = F × d = 200 N × 15 m = 3,000 J.
2. Student climbing rope: F = m × g = 55 × 10 = 550 N. W = 550 N × 4 m = 2,200 J.
3. Crane lifting beam: F = 2,000 × 10 = 20,000 N. W = 20,000 × 12 = 240,000 J (240 kJ). P = 240,000 ÷ 8 = 30,000 W (30 kW).
4. Light bulb energy: Time = 5 hours = 5 × 3,600 = 18,000 s. Energy in joules = P × t = 60 × 18,000 = 1,080,000 J (1.08 MJ). Energy in kWh = 0.060 kW × 5 h = 0.3 kWh.
Activity 2, Comparing Human and Machine Power
Experienced shearer: time = 2 min = 120 s. Energy = P × t = 200 × 120 = 24,000 J [0.5]. Power = 200 W (given) [0.5].
Beginner shearer: time = 6 min = 360 s. Energy = 200 × 360 = 72,000 J [0.5]. Power = 200 W (same machine) [0.5].
Both use the same power (200 W) because it is the same machine. But the beginner takes longer, so uses more total energy [1 mark]. The experienced shearer is more "productive", they do the same job (shear one sheep) using less time and therefore less total energy. The machine's power is fixed; the human's efficiency varies [1 mark].
Cost: Energy in kWh = 24,000 ÷ 3,600,000 = 0.0067 kWh. Cost = 0.0067 × $0.30 = $0.002 (experienced) [0.5]. Beginner: 72,000 ÷ 3,600,000 = 0.02 kWh. Cost = 0.02 × $0.30 = $0.006 [0.5]. The cost difference is small per sheep but significant over a day shearing hundreds of sheep.
Multiple Choice
1. CNo work is done because the box does not move. W = F × d = F × 0 = 0 J.
2. BF = 500 × 10 = 5,000 N. W = 5,000 × 8 = 40,000 J. P = 40,000 ÷ 4 = 10,000 W.
3. ASame work (same force, same distance), but Student A takes half the time so has twice the power. Option B confuses time with work. Option C confuses speed with work. Option D ignores time.
4. DEnergy = P × t. 2,000 W × 180 s = 360,000 J. 1,000 W × 360 s = 360,000 J. Same energy, different rates. Option A doubles incorrectly. Option B doubles incorrectly. Option C introduces irrelevant efficiency.
5. BEnergy input = 200 MJ ÷ 0.35 = 571 MJ (approx). Time = 200,000,000 ÷ 2,500,000 = 80 s. Option A ignores efficiency. Option C uses wrong time calculation. Option D miscalculates energy.
Short Answer Model Answers
Q6 (3 marks): F = 1,200 × 10 = 12,000 N [1 mark]. W = 12,000 × 250 = 3,000,000 J (3 MJ) [1 mark]. P = 3,000,000 ÷ 45 = 66,667 W (≈ 67 kW) [1 mark].
Q7 (4 marks): Unit A time = 18,000,000 J ÷ 2,500 W = 7,200 s = 2 hours [0.5]. Unit B time = 18,000,000 ÷ 5,000 = 3,600 s = 1 hour [0.5]. Unit A energy per hour = 2.5 kW × 1 h = 2.5 kWh [0.5]. Unit B energy per hour = 5 kW × 1 h = 5 kWh [0.5]. Unit B removes heat faster (1 hour vs 2 hours) but uses twice as much electricity per hour [1 mark]. In Darwin's climate with a long hot season, operating costs matter. If the house needs cooling 8 hours per day for 200 days: Unit A costs 2.5 × 8 × 200 × $0.30 = $1,200/year. Unit B costs 5 × 8 × 200 × $0.30 = $2,400/year. The $400 upfront saving of Unit A is recovered in less than 4 months [1 mark]. Recommendation depends on priorities: Unit B for faster cooling comfort, Unit A for long-term cost savings.
Q8 (5 marks): Diesel energy input = 200 MJ ÷ 0.35 = 571 MJ (≈ 571,000,000 J) [1 mark]. Electric energy input = 200 MJ ÷ 0.85 = 235 MJ (≈ 235,000,000 J) [1 mark]. Diesel time = 200,000,000 ÷ 2,500,000 = 80 s. Electric time = 200,000,000 ÷ 2,000,000 = 100 s [1 mark]. The claim is flawed because "more powerful" only means faster work, not better overall performance. The electric truck uses less than half the energy (235 MJ vs 571 MJ) to do the same job [1 mark]. Conclusion: "Better" depends on priorities. If speed matters most, the diesel truck is better (80 s vs 100 s). If energy cost and environmental impact matter most, the electric truck is dramatically better. The mining company's claim oversimplifies by focusing only on power, ignoring efficiency and total energy use [1 mark].
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