The human engine: food energy, work, power, efficiency and the simple machines that trade force for distance
By the end of this lesson you will be able to
- Describe the energy transfers when a person powers a machine, naming the store the energy leaves and the store it enters.
- Calculate work done, power and efficiency, with units and sensible significant figures.
- Explain why a simple machine can multiply a force but never the energy, and why its efficiency is always below 100 %.
- Calculate the mechanical advantage, velocity ratio and efficiency of a pulley system, a ramp and a lever.
- Analyse a bicycle as a system of simple machines driven by a human engine of about 25 % efficiency.
- Evaluate when human power is the right energy source for a machine, using data.
You met this before
- Energy is stored in stores — chemical, kinetic, gravitational potential, thermal, elastic — and is transferred between them; it is never created or destroyed (Year 1).
- Kinetic energy Ek = ½mv² (Year 1).
- Gravitational potential energy change ΔEp = mgΔh, in joules, with g at 9.8 N/kg (Year 1).
- Work done is force × distance moved in the direction of the force: W = Fd, and one joule is one newton metre.
- Power is the rate of transferring energy: P = E ÷ t, and 1 W = 1 J/s (Year 3 Circuits).
- Your cells release the energy in glucose by respiration; muscles turn some of it into movement and the rest heats you (Year 3 Biology).
A 60 kg student runs up a flight of stairs 3.0 m high in 4.0 s. Calculate the gravitational potential energy she gains and her useful power.
Reveal
ΔEp = mgΔh
ΔEp = 60 kg × 9.8 N/kg × 3.0 m
ΔEp = 1 764 J ≈ 1 800 J
P = E ÷ t
P = 1 764 J ÷ 4.0 s
P = 440 W (441 W)
That is a burst. Nobody can keep up 440 W of useful power for long — which is the whole story of this lesson.
Revise it in full: Year 1 · Energy · Lesson 2 — Kinetic and gravitational potential energy: putting numbers on the stores · Year 1 · Energy · Lesson 3 — Conservation of energy: the law nothing has ever broken · Year 3 · Biology · Unit 2 · Lesson 5 — Respiration: releasing the energy
The puzzle
A bicycle has no engine, no battery and no fuel tank, yet a rider on it travels three or four times faster than on foot and, per kilometre, uses less food energy than walking would.
At the same time, a typical fit adult can keep up only about 100–200 W of pedalling power for an hour. An electric kettle uses 2 000 W. It would take a team of about ten to twenty strong riders on generator bikes to boil it.
So the human body is a weak engine — and the bicycle is still the most efficient way humans have found to move themselves. How can both be true? The answer is in two words you will use all lesson: efficiency and machines.
A rider eats a 400 kJ banana. Predict roughly how much of that energy ends up pushing the pedals, and where the rest goes. Then predict: could a machine with gears let her lift a 500 kg car by pedalling? What would she have to “pay”?
Compare your answer
Muscles transfer only about a quarter of the chemical energy to useful work — around 100 kJ of the banana. The other three quarters heats her body (which is why she sweats) and is lost to the surroundings as thermal energy.
Yes, a machine could lift the car: a gear system, a lever or a pulley can multiply a force as much as you like. The price is distance. To lift 500 kg by 1 m (about 4 900 J) with a pedal force of 100 N she would have to push the pedals through about 49 m — more, allowing for friction. Machines trade force for distance; they never give energy away.
The science — structured notes
1.1 The human engine: chemical energy in, work and heat out
Food is a chemical store. Food labels give its energy in kilojoules (kJ) — and often also in kilocalories (1 kcal = 4.18 kJ). A banana carries about 400 kJ; an adult needs roughly 8 000–10 000 kJ a day.
Muscle cells release that energy by respiration and use it to contract. A muscle pulling on a bone does work on the outside world: it can lift your body (a gain in gravitational potential energy), speed up a bicycle (kinetic energy) or push against friction and air (which ends as thermal energy).
The human engine is not very efficient. For cycling and similar steady exercise, only about 20–25 % of the chemical energy released in the muscles becomes mechanical work; the other 75–80 % heats the body. Even at rest your body transfers about 80–100 W to its surroundings — the power of a bright old-fashioned light bulb.
“When a cyclist stops at the top of a hill, the energy from her breakfast has been used up.”
Reveal answer
False. The energy has been transferred, not used up. Part of it is in the gravitational potential store (she is higher up); most of it is in the thermal store of her body and the surrounding air. The total is unchanged — conservation of energy.
1.2 Work and power: how much, and how fast
When a force moves its point of application, it does work, and work done equals energy transferred:
W = F × d
F is the force in N and d the distance moved in the direction of the force in m; W is in joules. Lifting at a steady speed, the force equals the weight, so the work done against gravity is mgh.
Power is how fast the work is done:
P = W ÷ t
A watt is one joule per second. The same climb done twice as fast needs twice the power, but the same energy.
| Human activity | Useful mechanical power (approx.) | For how long |
|---|---|---|
| Sprint up stairs, jump, sprint on a bike | 1 000–2 000 W | a few seconds |
| Hard effort, trained cyclist | 300–400 W | up to about an hour |
| Steady cycling or treadling, fit adult | 75–150 W | hours |
| Hand-cranking (arms only) | 40–75 W | tens of minutes |
Legs beat arms because they contain the body’s biggest muscles. That is why pedal-powered machines — bicycles, treadle pumps, pedal grain mills — outperform hand-cranked ones.
A porter carries a 25 kg bag of maize meal up stairs with a vertical rise of 6.0 m in 30 s. Calculate the work done on the bag and the useful power.
Force needed = weight of bag
F = mg = 25 kg × 9.8 N/kg
F = 245 N
W = F × d
W = 245 N × 6.0 m
W = 1 470 J ≈ 1 500 J
P = W ÷ t
P = 1 470 J ÷ 30 s
P = 49 W
This is only the power delivered to the bag. The porter also lifts his own 65 kg body, a further 3 822 J, so his legs deliver about 176 W in total — useful work on the bag is just over a quarter of it.
A 70 kg cyclist on a 10 kg bicycle rides up a long hill, gaining 120 m of height in 10 minutes. Her muscles transfer 24 % of the chemical energy they release into work. (1) Calculate the useful power against gravity. (2) Calculate the chemical energy she uses for the climb, ignoring friction and air resistance, and compare it with a 400 kJ banana.
(1) Total mass m = 70 kg + 10 kg = 80 kg
ΔEp = mgΔh
ΔEp = 80 kg × 9.8 N/kg × 120 m
ΔEp = 94 080 J
t = 10 min = 600 s
P = 94 080 J ÷ 600 s
P = 157 W ≈ 160 W
(2) Useful energy = 0.24 × chemical energy
chemical energy = 94 080 J ÷ 0.24
chemical energy = 392 000 J ≈ 390 kJ
Almost exactly one banana — for gravity alone. Friction and air resistance add more, and the extra 298 kJ of heat is why she arrives dripping with sweat.
A water carrier lifts a 20 L container (20 kg) from the ground onto her head, 1.6 m up, 30 times in a morning, and does it in a total of 60 s of lifting. Calculate the total work done on the water and the average power during the lifts.
Reveal answer
Work per lift = mgh
Work per lift = 20 kg × 9.8 N/kg × 1.6 m
Work per lift = 313.6 J
Total work = 30 × 313.6 J
Total work = 9 400 J (9 408 J)
P = 9 408 J ÷ 60 s
P = 160 W (157 W)
A fit adult’s working rate, done with the arms and back — which is why carrying water is exhausting.
1.3 Efficiency and Sankey diagrams
No machine turns all the energy supplied into the output you want. The rest is wasted — usually as thermal energy from friction, sometimes as sound. Efficiency measures the useful fraction:
efficiency = (useful energy out ÷ total energy in) × 100 %
The same formula works with powers instead of energies. Efficiency has no unit and can never exceed 100 %.
When energy passes through several stages, multiply the efficiencies (as decimals) to get the overall efficiency. A bicycle chain in good condition is about 95–98 % efficient, so almost all the loss happens inside the rider.
A rider’s muscles release chemical energy at 500 W and are 24 % efficient. The chain and gears are 96 % efficient. Calculate the power delivered to the rear wheel and the overall efficiency.
Power at the pedals = 0.24 × 500 W
Power at the pedals = 120 W
Power at the wheel = 0.96 × 120 W
Power at the wheel = 115 W (115.2 W)
Overall efficiency = 115.2 W ÷ 500 W × 100 %
Overall efficiency = 23 %
Check by multiplying: 0.24 × 0.96 = 0.23
The drivetrain wastes under 5 W as heat in the chain; the rider’s body wastes 380 W.
“The pump lifted water with 180 J of useful energy while the person treadling it did 450 J of work. Efficiency = 450 ÷ 180 = 2.5, so 250 %.”
Reveal answer
The fraction is upside down. Useful out goes on top:
efficiency = 180 J ÷ 450 J × 100 %
efficiency = 40 %
An efficiency over 100 % would mean the pump creates energy — impossible by conservation of energy.
1.4 Simple machines: force multipliers, not energy multipliers
A simple machine changes the size or direction of a force. The classic set is the lever, the wheel and axle, the pulley, the inclined plane (ramp), the wedge and the screw; gears are wheels and axles that push on each other.
Each lets a small effort move a large load. The catch is the distances. For an ideal (frictionless) machine, the work put in equals the work got out:
effort × distance moved by effort = load × distance moved by load
So if the effort is a quarter of the load, it must move four times as far. Energy is conserved; force is not.
Three numbers describe a machine:
- Mechanical advantage MA = load ÷ effort (how much the force is multiplied).
- Velocity ratio VR = distance moved by effort ÷ distance moved by load (set by the geometry alone; also called the distance ratio).
- Efficiency = MA ÷ VR × 100 %.
MA and VR have no units. Friction and the weight of moving parts always make MA smaller than VR, so real machines are less than 100 % efficient.
A mechanic uses a block and tackle with four rope sections supporting the lower block to lift a 1 200 N engine by 0.50 m. She pulls with 360 N. Calculate the velocity ratio, the mechanical advantage, the efficiency and the length of rope she must pull through.
VR = number of supporting sections
VR = 4
MA = load ÷ effort
MA = 1 200 N ÷ 360 N
MA = 3.33
efficiency = MA ÷ VR × 100 %
efficiency = 3.33 ÷ 4 × 100 %
efficiency = 83 %
rope pulled = VR × load distance
rope pulled = 4 × 0.50 m
rope pulled = 2.0 m
Check with energy: work in = 360 N × 2.0 m = 720 J
work out = 1 200 N × 0.50 m = 600 J
600 J ÷ 720 J = 0.83 — the same 83 %
Explain why the efficiency of a pulley system is always less than 100 %, and why adding more pulleys raises the velocity ratio but can lower the efficiency.
Reveal answer
Some of the work done by the effort is done against friction in the pulley bearings and in bending the rope, and some lifts the movable block itself; that energy ends in the thermal store (or as GPE of the block), not in the load, so useful work out is less than work in.
Each extra pulley adds another supporting section (higher VR) but also adds another bearing to overcome and more weight in the lower block. Beyond a few pulleys the extra friction grows faster than the benefit, so MA ÷ VR falls.
1.5 The ramp: the oldest machine
An inclined plane lets you raise a load by pushing it along a slope instead of lifting it straight up. The load still gains mgh, but the effort acts over the longer slope length L, so it can be smaller.
VR = L ÷ h
A longer, gentler ramp has a bigger VR and needs less effort — but you walk further. This is why mountain roads zig-zag and why building codes set a maximum slope for wheelchair ramps (often about 1 in 12).
A wheelchair and its user weigh 900 N. A ramp 6.0 m long rises 0.50 m to a clinic door. A helper pushes along the slope with a force of 95 N. Calculate the ideal (frictionless) effort, the efficiency, and the energy wasted.
Work out (useful) = load × height
Work out = 900 N × 0.50 m = 450 J
Ideal effort = 450 J ÷ 6.0 m
Ideal effort = 75 N
Work in = 95 N × 6.0 m = 570 J
efficiency = 450 J ÷ 570 J × 100 %
efficiency = 79 %
wasted = 570 J − 450 J
wasted = 120 J, to the thermal store (rolling friction, bearings)
The clinic replaces the ramp with a shorter one, 3.0 m long, to the same door. Predict the ideal effort now, and explain whether the energy the helper must supply goes up or down.
Reveal answer
Ideal effort = 450 J ÷ 3.0 m
Ideal effort = 150 N — twice as much
The useful energy is still 450 J (same load, same height). With a shorter ramp there is less distance for friction to act over, so the total energy supplied may even fall slightly — but the force needed doubles, and for many helpers and self-propelled users that makes the ramp unusable. The trade-off is force against distance, not energy.
1.6 The bicycle: a human engine driving a chain of machines
A bicycle is a system of simple machines driven by the most flexible engine there is. The pedal and crank form a wheel and axle; the chainring and rear sprocket are gears joined by a chain; the rear hub and wheel are another wheel and axle.
Unlike a pulley, a bicycle is built to lose force and gain distance. Your foot moves round a circle of about 1.1 m per crank turn, while the bike moves 5–8 m. So the forward push of the tyre on the road is much smaller than your foot’s force — but it moves much further and faster.
Count the gear teeth to find how many times the wheel turns per turn of the cranks:
wheel turns per crank turn = chainring teeth ÷ sprocket teeth
With 44 and 16 teeth that is 2.75. On a 2.1 m circumference wheel the bike moves 5.8 m for every crank turn. Lesson 3 uses torque to explain why a low gear (small chainring, big sprocket) makes hills possible.
A rider pushes on the pedals with an average force of 150 N around a crank circle of circumference 1.10 m. In the gear above the bicycle moves 5.8 m per crank turn, and the drivetrain is 95 % efficient. Estimate the average forward force of the tyre on the road.
Work in per crank turn = 150 N × 1.10 m
Work in = 165 J
Work out = 0.95 × 165 J
Work out = 156.75 J
Forward force = work out ÷ distance
Forward force = 156.75 J ÷ 5.8 m
Forward force = 27 N
The bicycle has a mechanical advantage of 27 ÷ 150 = 0.18 — far below 1. It is a distance multiplier: small push on the road, large distance and speed.
On the flat at 25 km/h a rider must overcome about 20 N of air resistance and rolling friction. Calculate the useful power needed, and the food energy per hour if her muscles are 24 % efficient and the drivetrain 96 % efficient.
Reveal answer
v = 25 ÷ 3.6 = 6.94 m/s
P = F × v (work per second = force × distance per second)
P = 20 N × 6.94 m/s
P = 139 W at the wheel
Chemical power = 139 W ÷ (0.24 × 0.96)
Chemical power = 603 W
Energy per hour = 603 W × 3 600 s
Energy per hour = 2.2 × 10⁶ J = 2.2 MJ — about five bananas
P = Fv is W = Fd divided by t; it is the formula for any vehicle moving steadily against a resistive force.
Try it — how does your body respond to delivering steady mechanical power?
In the step test a student steps up onto a box and down again in time to a metronome, and a partner counts the pulse for 15 s at the end of every minute. The physics is in the stepping: each step up lifts the whole body through the box height, so the step rate sets a steady useful power. The heart rate shows the human engine raising its supply of oxygen to match.
work per step = mgh
work per step = 50 kg × 9.8 N/kg × 0.20 m
work per step = 98 J
P = 98 J ÷ 2.0 s
P = 49 W
On the 30 cm box it is 74 W. With muscles about 20–25 % efficient, the chemical power needed is roughly 200–370 W on top of the resting rate.
Common mistakes to avoid
- “Energy is used up” or “lost”. It is transferred — name the store it goes to (usually the thermal store of the surroundings).
- One energy form only. A transfer needs two: “chemical → kinetic”, not just “kinetic”.
- Efficiency upside down. Useful out ÷ total in; if you get more than 100 %, you divided the wrong way.
- Mixing kJ and J, or minutes and seconds. Convert first: 10 min = 600 s, 390 kJ = 390 000 J.
- “A machine gives you more energy.” It can multiply force, never energy. Work out ≤ work in.
- MA and VR confused. MA is about forces (load ÷ effort); VR is about distances (effort distance ÷ load distance).
- Power confused with energy. Power is joules per second; a watt is not a “unit of energy”.
- Distance not along the force. For a vertical lift use the height, not the length of a slope.
Study smart: how this is examined
Study routine. Today: redraw the Sankey diagram of the human engine and the pulley diagram from memory, with every number. In two days: do the porter, the long-climb and the wheelchair-ramp EXAMPLES with the notes closed. In a week: run the step test lab, calculate your own stepping power, and take the quiz.
How we found out — machines that cannot cheat, and the fire inside us
Archimedes of Syracuse (about 287–212 BCE) worked out the law of the lever and is said to have boasted, “Give me a place to stand and I will move the Earth.” Three centuries later Hero of Alexandria described five simple machines — the lever, the windlass (wheel and axle), the pulley, the wedge and the screw — and how they could be combined.
What nobody could say clearly was why a machine could not give something for nothing. Galileo Galilei, in his short treatise Le Mecaniche (written around 1600), argued that whatever a machine gains in force it loses in distance or time: nature cannot be cheated.
That idea became the principle of work, and in the 1840s James Joule‘s measurements turned it into the conservation of energy.
The engine inside us was understood around the same time as the steam engine. In 1782–1783 Antoine Lavoisier and Pierre-Simon Laplace put a guinea pig inside an ice calorimeter and compared the ice it melted with the carbon dioxide it breathed out. The ratio matched burning charcoal: respiration, Lavoisier concluded, is a slow combustion.
A century later Wilbur Atwater in the United States built a room-sized respiration calorimeter in which a person could live and exercise for days. He measured food energy in and heat and work out, and showed that the human body obeys the conservation of energy. His “Atwater factors” (about 17 kJ per gram of carbohydrate or protein, 37 kJ per gram of fat) still underlie the kilojoules on food labels.
Galileo said a machine cannot “cheat nature”. Explain what he meant using the pulley system of Section 1.4.
Reveal answer
The pulley lets a 200 N effort (ideally) lift a 400 N load, so the force is multiplied by 2 — but the effort must pull 2 m of rope to lift the load 1 m.
Work in (200 N × 2 m, 400 J) equals work out (400 N × 1 m, 400 J) at best, and friction makes work out smaller. The machine multiplies force by dividing distance; it never supplies extra energy.
Where it is used now
- Treadle pumps. Across East and Southern Africa and South Asia, farmers lift irrigation water from shallow wells and rivers with foot-operated treadle pumps — the legs being the strongest muscles — watering vegetable plots in the dry season without fuel.
- Wind-up radios. In the early 1990s the British inventor Trevor Baylis designed a clockwork radio so that people without mains power or batteries could hear public-health broadcasts; it went into production in Cape Town in the mid-1990s. Hand-crank torches and phone chargers follow the same idea.
- Load-carrying bicycles. Charity-built heavy-duty bicycles carry children to school, milk to market and health workers to villages in rural Zambia, Kenya, Malawi and elsewhere; a bicycle can carry several times the load a person can carry on foot.
- Hoists and ramps. Garages lift engines with block-and-tackle hoists; builders move wheelbarrows up plank ramps; accessibility laws set ramp slopes so a wheelchair user can manage the effort.
- Sports science. Power meters in pedals and cranks measure a cyclist’s power in watts many times a second, letting coaches pace riders precisely and detect fatigue.
Science now — and the scientist you need to be
What is happening in 2026
Human power has not gone away; it has been joined. Electric-assist bicycles (e-bikes), where a motor adds to the rider’s own power, are now among the fastest-growing kinds of vehicle in many cities, and e-cargo bikes deliver parcels in crowded centres. Design choices are all about the physics of this lesson: motor power, battery energy, efficiency and mass.
Powered exoskeletons that assist the hip or back are being tested in warehouses and in rehabilitation after stroke; they work by adding torque at a joint at the right moment of each step.
Wearable power meters, heart-rate straps and AI coaching apps now estimate a rider’s efficiency and fatigue from the data, but they still rest on W = Fd and P = E ÷ t.
Careers here run from mechanical and biomedical engineering to sports science, physiotherapy and product design for low-income markets, where a well-designed human-powered machine can outperform a fuel-hungry one.
The mindshift
What you need to be able to do
Name two energy forms in every transfer. Calculate work, power and efficiency with units, and multiply efficiencies along a chain. Find MA, VR and efficiency of a machine from forces and distances. And decide — with numbers — when a human-powered machine is the right tool.
See an example
16 steps of 0.17 m give a vertical height of 2.72 m, climbed in 3.2 s by a 55 kg student.
P = mgh ÷ t
P = 55 kg × 9.8 N/kg × 2.72 m ÷ 3.2 s
P = 460 W
A careful assistant uses the vertical height; one that multiplies by the length along the stairs overestimates the work, because the weight acts vertically.
Key terms
| Work done | Energy transferred when a force moves an object in the direction of the force; W = Fd, in joules. |
| Power | The rate of doing work or transferring energy; P = E ÷ t, in watts (1 W = 1 J/s). |
| Efficiency | Useful energy (or power) out ÷ total energy (or power) in × 100 %; always less than 100 %. |
| Sankey diagram | An energy-flow diagram whose arrow widths are proportional to the energy or power in each path. |
| Simple machine | A device that changes the size or direction of a force: lever, wheel and axle, pulley, inclined plane, wedge, screw. |
| Load and effort | The force the machine overcomes, and the force applied to the machine. |
| Mechanical advantage (MA) | Load ÷ effort; how many times the machine multiplies the force. |
| Velocity ratio (VR) | Distance moved by the effort ÷ distance moved by the load; fixed by the geometry. |
| Human engine | The muscles, releasing chemical energy by respiration; about 20–25 % efficient at producing work. |
| Gear ratio | For a bicycle, chainring teeth ÷ sprocket teeth = wheel turns per crank turn. |
Think like a scientist
Criterion D A women’s farming cooperative grows vegetables on land beside a river. In the dry season the plots need 10 m³ (10 000 kg) of water a day, lifted 5.0 m from the river to a storage tank. They can buy either:
- Two treadle pumps — 1 800 pula each; about 40 % efficient; worked by one person at a time delivering 75 W of mechanical power.
- A solar pump — 16 000 pula with its 300 W panel; the panel gives about 250 W in full sun and the pump is 45 % efficient; no fuel, but a two-year payback loan is needed.
(a) Calculate the useful energy needed each day to lift the water. [2]
(b) Calculate how many hours of treadling a day this needs, and how many hours of full sun the solar pump needs. [3]
(c) Calculate the extra food energy per day the treadlers need, if their muscles are 25 % efficient, and compare it with a 400 kJ banana. [2]
(d) Discuss and evaluate which option the cooperative should choose. Use your calculations and include implications in at least three of economic, social, environmental and health categories, a justified conclusion and one limitation of the data. [8]
Model answer
(a)
E = mgh
E = 10 000 kg × 9.8 N/kg × 5.0 m
E = 490 000 J = 490 kJ [2]
(b) Treadle: useful power = 0.40 × 75 W = 30 W [1]
t = 490 000 J ÷ 30 W
t = 16 300 s ≈ 4.5 hours of treadling [1]
Solar: useful power = 0.45 × 250 W = 112.5 W
t = 490 000 J ÷ 112.5 W
t = 4 360 s ≈ 1.2 hours of full sun [1]
(c) Work by the legs = 75 W × 16 300 s
Work by the legs = 1.22 MJ
Food energy = 1.22 MJ ÷ 0.25
Food energy = 4.9 MJ ≈ 12 bananas a day, shared among the treadlers [2]
(d) Science [1]: both lift the same 490 kJ; the difference is the source of the input energy and its efficiency — muscles at 25 % and treadle at 40 % give about 10 % from food to water, while the sun is free once the panel is paid for.
Economic [1]: treadles cost 3 600 pula with no loan, but 4.5 hours of labour a day is time not spent weeding, selling or at school; the solar pump costs 16 000 pula and a loan, but frees that time and can water more land.
Social and health [2]: 4.9 MJ a day of extra food is significant for households who may already be short of food; treadling for hours in dry-season heat is hard physical work, often falling on women and girls. The solar pump’s water arrives in the middle of the day.
Environmental [1]: neither burns fuel; the panel’s manufacture has an energy and materials cost, and a pump that runs directly from the panel, with no battery, avoids battery waste. Both avoid a diesel pump’s emissions.
Conclusion [2]: for example — buy one treadle pump now and save for the solar pump, because the treadle is affordable without debt and the water is needed this season; move to solar when the cooperative can afford it, because freeing 4.5 hours of labour a day is worth more than the pump costs.
Or: take the loan at once, because the labour and food costs of treadling exceed the loan repayments. Either is credited if justified with the numbers.
Limitation [1]: “full sun” hours vary with season and cloud, and the 75 W assumes a fit adult working steadily — real output falls with heat and fatigue, so the treadling time is probably underestimated.
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
A worker lifts a 25 kg sack onto a truck bed 1.2 m high. Calculate the work done on the sack.
Reveal answer
W = mgh
W = 25 kg × 9.8 N/kg × 1.2 m [1]
W = 294 J ≈ 290 J [1]
Select the correct energy forms to complete the chain for a cyclist who starts from rest and rides to the top of a hill, where she stops: ______ → kinetic energy → ______.
Reveal answer
Chemical (potential) energy [1] → kinetic energy → gravitational potential energy [1]. (Thermal energy of the surroundings is also produced throughout, but the question asks for the main chain.)
A rider’s muscles release chemical energy at 600 W and she delivers 140 W to the pedals. Calculate her efficiency and the power transferred to the thermal store, and state where that energy goes.
Reveal answer
efficiency = 140 W ÷ 600 W × 100 %
efficiency = 23 % [1]
thermal = 600 W − 140 W
thermal = 460 W [1]
It heats her body and is transferred to the surrounding air by sweating, breathing and convection [1].
A pulley system has a velocity ratio of 3. An effort of 180 N lifts a load of 450 N. Calculate the mechanical advantage, the efficiency, and how far the effort moves to lift the load 2.0 m.
Reveal answer
MA = 450 N ÷ 180 N
MA = 2.5 [1]
efficiency = 2.5 ÷ 3 × 100 %
efficiency = 83 % [1]
effort distance = 3 × 2.0 m
effort distance = 6.0 m [1]
Explain why the mechanical advantage of a real machine is always less than its velocity ratio.
Reveal answer
If MA equalled VR the work in would equal the work out; in a real machine some input work is done against friction (and lifting moving parts), transferred to the thermal store [1], so a larger effort is needed than the ideal, making MA = load ÷ effort smaller than VR [1].
A delivery rider must get a loaded cart up a step 0.40 m high. Outline, using ideas about work, why pushing it up a 4.0 m plank is easier than lifting it, and state the minimum effort for a 600 N cart.
Reveal answer
The useful work is the same either way: 600 N × 0.40 m = 240 J [1]. On the plank the effort acts over 4.0 m instead of 0.40 m, so a smaller force does the same work [1].
minimum effort = 240 J ÷ 4.0 m
minimum effort = 60 N (friction ignored) [1]
7. A cyclist and bicycle (total 80 kg) climb a steady slope at 3.0 m/s along the road. The rider can deliver 200 W to the wheel. Ignoring air resistance and friction, calculate the rate at which she gains height and the steepest slope (as an angle) she can climb at this speed.
Reveal answer
All 200 W goes into gravitational potential energy, so power = mg × (vertical speed) [1]:
vertical speed = P ÷ mg
vertical speed = 200 W ÷ (80 kg × 9.8 N/kg)
vertical speed = 0.255 m/s [1]
sin θ = vertical speed ÷ speed along the road
sin θ = 0.255 ÷ 3.0 = 0.085 [1]
θ = 4.9° (a gradient of about 8.5 %) [1]
8. On summit day a climber with her pack (80 kg in total) rises 1 200 m. Her muscles are 20 % efficient at doing work against gravity. Calculate the food energy used for the height gain alone, how many 250 kJ energy bars that is, and explain why the true figure is much larger.
Reveal answer
ΔEp = 80 kg × 9.8 N/kg × 1 200 m
ΔEp = 940 800 J [1]
food energy = 940 800 J ÷ 0.20
food energy = 4.7 × 10⁶ J = 4.7 MJ [1]
bars = 4 700 kJ ÷ 250 kJ
bars = 19 [1]
The true figure is larger because she also needs her resting (basal) power, about 80–100 W for all the hours of the climb, plus energy for keeping warm at altitude and for the work of moving her legs even on the level; none of this appears in mgh [1].
Summary
- The human body is an engine: chemical energy from food, released by respiration, becomes work at about 20–25 % efficiency; the rest heats the body and the surroundings.
- Work W = Fd, in J.
- Power P = E ÷ t, in W.
- Efficiency = useful out ÷ total in × 100 %, always below 100 %; multiply efficiencies along a chain.
- A fit adult keeps up about 75–150 W of useful power for hours, a trained cyclist 300–400 W for an hour; legs beat arms.
- Simple machines multiply force at the cost of distance: effort × effort distance ≥ load × load distance.
- MA = load ÷ effort; VR = effort distance ÷ load distance.
- Efficiency = MA ÷ VR × 100 %.
- A bicycle is a chain of machines that trades force for distance and speed; the gear ratio (chainring teeth ÷ sprocket teeth) gives wheel turns per crank turn.
Next time → Levers and moments: the turning effect of a force, the principle of moments, the three classes of lever and the levers inside your own arm.