Senior 1 practice book · Unit 5 of 9

Work, Power and Energy

50 questions that complete the Senior 1 quiz for this unit: 31 core and 19 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Holding a heavy load still is hard work, so a lot of work is done on it.In physics work is done only when a force moves something in the direction of the force. Holding a load still at the same height does no work on the load, although your muscles get tired.
Energy gets used up and disappears.Energy is never destroyed; it changes form. 'Used' energy usually ends up as heat spread into the surroundings, where it is hard to use again.
A kilowatt-hour is a unit of power.The kilowatt-hour is a unit of ENERGY: the energy used by a 1 kW appliance in 1 hour, equal to 3 600 000 J. Power is measured in watts.
Doubling the speed doubles the kinetic energy.KE = ½mv², so kinetic energy depends on the SQUARE of the speed: doubling the speed makes the KE four times bigger.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Work: W = F × d, its unit, and when no work is done
Forms of energy
Kinetic energy: KE = ½mv²
Gravitational potential energy: PE = mgh
Energy transformations in devices and daily life
Conservation of energy; PE ↔ KE changes
Power: P = W/t and E = Pt
Renewable and non-renewable energy sources in Rwanda
Efficiency of machines and Sankey (energy flow) diagrams
The kilowatt-hour and the cost of electricity
Saving energy and environmental effects of energy sources

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 19 harder ones are marked ★ Challenge.

1True or false
A loudspeaker changes electrical energy mainly into sound energy.
Show answer
Answer: True
Electrical signals make the speaker cone vibrate and produce sound (with some heat).
Common mistakeLearners confuse it with a microphone, which does the opposite change.
2True or false · ★ Challenge
When you hold a heavy bag still above your head, you do no work on the bag, even though you feel tired.
Show answer
Answer: True
The bag does not move, so the distance is zero and W = F × 0 = 0; your muscles use energy internally.
Common mistakeFeeling tired makes learners think work is being done on the bag, but work needs movement in the direction of the force.
3True or false
Improved cooking stoves save firewood because they waste less heat.
Show answer
Answer: True
They keep the heat around the pot, so more of the fuel's energy cooks the food and less fuel is needed.
Common mistakeLearners think the saving comes from cooking food faster; it comes from wasting less heat.
4Multiple choice · ★ Challenge
Firewood counts as a renewable source of energy only if:
1. AIt is burned in a closed stove indoors
2. BNew trees are planted as fast as trees are cut
3. CIt is cut from very old trees in forests
4. DIt is dried in the sun before burning
Show answer
Answer: B. New trees are planted as fast as trees are cut
A source is renewable if it is replaced naturally as fast as it is used; cutting trees faster than they regrow uses up forests.
Common mistakeDrying wood helps it burn better, but it does not make the source renewable.
5True or false
On an electricity bill, the units being charged for are kilowatts of power.
Show answer
Answer: False
Bills charge for energy in kilowatt-hours (power × time), not for kilowatts of power.
Common mistakeThe word 'kilowatt' inside 'kilowatt-hour' makes learners think it is a power unit.
6Fill in the blank
At the highest point of its swing, the energy of a pendulum bob is all ______ energy.
Show answer
Answer: (gravitational) potential
At the top the bob is momentarily at rest, so its KE is zero and its energy is potential energy.
Common mistakeWriting 'kinetic' forgets that the bob stops for an instant at the end of each swing.
7True or false
Real machines are always less than 100% efficient because some energy is transferred to wasted forms such as heat.
Show answer
Answer: True
Friction and electrical resistance always turn some energy into heat, so the useful output is less than the input.
Common mistakeSome learners think a new or well-oiled machine is 100% efficient; friction can be reduced but never removed.
8Multiple choice · ★ Challenge
A cyclist's dynamo lights the bicycle lamp. Which chain of energy changes is correct?
1. AKinetic → chemical (food) → electrical → light and heat
2. BChemical (food) → kinetic → electrical → light and heat
3. CElectrical → kinetic → chemical (food) → light and heat
4. DChemical (food) → electrical → kinetic → light and heat
Show answer
Answer: B. Chemical (food) → kinetic → electrical → light and heat
Food energy lets the cyclist pedal (kinetic), the dynamo turns kinetic into electrical energy, and the lamp gives light and heat.
Common mistakePutting electrical before kinetic reverses the dynamo; a dynamo needs movement to make electricity.
9Fill in the blank
1 kilowatt = ______ watts.
Show answer
Answer: 1000
The prefix kilo means 1000.
Common mistakeLearners confuse kilowatt with kilowatt-hour; 1 kW is a power of 1000 W.
10Multiple choice · ★ Challenge
Which Rwandan energy source gets its energy from the Sun indirectly, through the water cycle?
1. AMethane from Lake Kivu
2. BPeat from the marshes
3. CImported diesel fuel
4. DHydroelectric power
Show answer
Answer: D. Hydroelectric power
The Sun evaporates water, which falls as rain on high ground and fills rivers that drive hydro turbines.
Common mistakeMethane is tempting because it is local, but it is a fuel formed from decayed matter, not part of the water cycle.
11True or false
A bus parked at the bus park has kinetic energy because it has a large mass.
Show answer
Answer: False
Kinetic energy depends on speed; a parked bus has v = 0, so KE = 0 however large its mass.
Common mistakeLearners link 'big and heavy' with energy, but kinetic energy needs motion.
12Multiple choice · ★ Challenge
If the speed of a car is tripled, its kinetic energy becomes:
1. A3 times as large
2. B6 times as large
3. C27 times as large
4. D9 times as large
Show answer
Answer: D. 9 times as large
KE ∝ v², so tripling v multiplies KE by 3² = 9.
Common mistake'3 times' forgets that the speed is squared in KE = ½mv².
13Fill in the blank
The energy stored in a stretched catapult rubber or a bent bow is called ______ potential energy.
Show answer
Answer: elastic (strain)
Stretched or squashed materials store elastic potential energy.
Common mistakeLearners write 'gravitational', but nothing has been lifted; the energy is stored by the change of shape.
14Fill in the blank
Kinetic energy is proportional to the ______ of the speed.
Show answer
Answer: square
KE = ½mv², so KE depends on v².
Common mistakeLearners write 'size' or 'double'; the key point is that the speed is squared.
15Fill in the blank
Efficiency = (useful energy output ÷ total energy ______) × 100%.
Show answer
Answer: input
Efficiency compares the useful energy out with all the energy put in.
Common mistakeWriting 'output' at the bottom would always give 100% or more.
16Fill in the blank · ★ Challenge
A 1000 W heater left on for one hour transfers ______ J; electricity companies call this amount one unit (1 kWh).
Show answer
Answer: 3 600 000 (3.6 × 10⁶)
1 kWh = 1000 W × 3600 s = 3 600 000 J.
Common mistakeLearners write 1000 J, forgetting that an hour has 3600 seconds.
17Multiple choice
Which pair are BOTH forms of stored (potential) energy?
1. AKinetic and sound
2. BChemical and elastic
3. CLight and kinetic
4. DSound and thermal
Show answer
Answer: B. Chemical and elastic
Chemical energy (in food, fuel, batteries) and elastic energy (in a stretched spring) are stored until released.
Common mistakeKinetic energy is tempting, but it is the energy of movement, not stored energy.
18Short answer · ★ Challenge
Give one advantage and one disadvantage of extracting methane gas from Lake Kivu to generate electricity.
Show answer
Model answer: Advantage: it uses a local fuel instead of imported diesel, and removing the gas reduces the danger of a sudden gas eruption from the lake. Disadvantage: burning methane releases carbon dioxide, which adds to global warming, and the gas will eventually run out (non-renewable).
Common mistakeLearners call methane renewable because it comes from a lake; it is a fuel that is used up when burned.
19Multiple choice
A pendulum bob swings to and fro. At the lowest point of its swing it has:
1. AMost kinetic energy and least potential energy
2. BMost potential energy and least kinetic energy
3. CNo kinetic energy and no potential energy at all
4. DNo kinetic energy but the most potential energy
Show answer
Answer: A. Most kinetic energy and least potential energy
At the lowest point the bob is moving fastest (most KE) and is at its lowest height (least PE).
Common mistakeLearners reverse the ends of the swing and the middle; the bob stops for an instant at the ends, not at the bottom.
20Multiple choice
What is the main energy change while a mobile phone battery is being charged?
1. AChemical → electrical
2. BLight → electrical
3. CKinetic → chemical
4. DElectrical → chemical
Show answer
Answer: D. Electrical → chemical
While charging, electrical energy from the charger is stored as chemical energy in the battery.
Common mistake'Chemical → electrical' is what happens when the phone is being USED, not charged.
21Multiple choice · ★ Challenge
A salesman claims his new generator has an efficiency of 125%. Why is this impossible?
1. AEfficiency is always measured in joules, not per cent
2. BGenerators can only reach 50% efficiency at best
3. CElectrical energy cannot be measured accurately
4. DThe useful output would exceed the energy put in
Show answer
Answer: D. The useful output would exceed the energy put in
Energy cannot be created, so the useful output can never be more than the input; efficiency is at most 100%.
Common mistakeThinking a better design could beat 100% ignores the law of conservation of energy.
22Fill in the blank
Gravitational potential energy depends on the mass, the gravitational field strength g and the ______ of the object.
Show answer
Answer: height
PE = mgh, so a higher position stores more energy.
Common mistakeLearners write 'speed', which affects kinetic energy, not potential energy.
23Multiple choice
What is a main environmental problem caused by using firewood and charcoal for cooking?
1. AIt makes the climate of the country much colder
2. BCutting trees causes deforestation and erosion
3. CIt increases the water in the lakes and rivers
4. DIt produces radioactive waste in the kitchen
Show answer
Answer: B. Cutting trees causes deforestation and erosion
Cutting trees faster than they regrow removes forests, and bare hillsides lose their soil when it rains.
Common mistakeLearners may think of radioactive waste, but that comes from nuclear power, not from burning wood.
24Short answer · ★ Challenge
A village must choose between a diesel generator and a small hydro plant on a nearby river. Give two arguments for the hydro plant and one possible problem with it.
Show answer
Model answer: For hydro: the river's energy is renewable and free once the plant is built; it gives no smoke or carbon dioxide, and there is no need to buy and transport diesel. Problem: the flow may fall in the dry season, reducing the power, and the plant costs more to build at first.
Common mistakeLearners only give 'it is cheaper'; good answers compare running cost, pollution and reliability.
25Multiple choice
Which of these is a unit of power?
1. AJ × s
2. BN × m
3. CJ/s
4. DkWh
Show answer
Answer: C. J/s
Power = energy ÷ time, so its unit is the joule per second (J/s), called the watt.
Common mistakekWh is tempting because it contains 'kilowatt', but it is a unit of energy.
26Short answer · ★ Challenge
A dropped ball bounces lower and lower each time. Explain where its energy goes. Does this break the law of conservation of energy?
Show answer
Model answer: At each bounce some energy is changed into heat (in the ball and floor) and sound, and some is lost to air resistance, so less is left as kinetic and then potential energy, and the ball rises less high. The total energy is still the same, so the law is not broken; energy is only spread into less useful forms.
Common mistakeLearners say the energy is 'used up'; it is transferred to the surroundings, not destroyed.
27Multiple choice
One joule is the work done when:
1. AA mass of 1 kg is lifted up through a height of 1 m
2. BA force of 1 N acts on an object for a time of 1 s
3. CA machine of power 1 W runs for a time of 1 hour
4. DA 1 N force moves something 1 m in its direction
Show answer
Answer: D. A 1 N force moves something 1 m in its direction
W = F × d, so 1 J = 1 N × 1 m.
Common mistakeLifting 1 kg through 1 m needs 10 J on Earth, because the weight of 1 kg is 10 N.
28Multiple choice · ★ Challenge
A 100 W television is used for 5 hours a day for 30 days. If electricity costs 250 FRW per kWh, what is the cost?
1. A3 750 000 FRW
2. B125 FRW
3. C15 FRW
4. D3750 FRW
Show answer
Answer: D. 3750 FRW
E = 0.1 kW × 5 h × 30 = 15 kWh; cost = 15 × 250 = 3750 FRW.
Common mistake3 750 000 FRW uses 100 instead of 0.1 kW; watts must be changed to kilowatts first.
29Short answer
Give two advantages and one disadvantage of solar home systems for rural Rwandan families.
Show answer
Model answer: Advantages: sunlight is free and renewable; no fuel needs to be bought; no smoke or pollution; works far from the national grid. Disadvantage: little or no power on cloudy days or at night unless batteries are charged; the panels and batteries cost money to buy and replace.
Common mistakeLearners list 'it is cheap' only; the panels cost money at first, it is the energy that is free.
30Multiple choice
A Sankey diagram for a filament lamp shows 100 J going in and 10 J coming out as light. What does the other arrow show?
1. A90 J of heat
2. B90 J of light
3. C10 J of heat
4. D110 J of heat
Show answer
Answer: A. 90 J of heat
Energy is conserved: 100 − 10 = 90 J, which is wasted as heat.
Common mistake110 J adds the light to the input; the outputs must ADD UP to the input.
31Multiple choice · ★ Challenge
A porter carries a 20 kg sack on his head and walks 50 m along a level road at steady speed. How much work does he do against gravity on the sack?
1. A0 J
2. B10 000 J
3. C1000 J
4. D200 J
Show answer
Answer: A. 0 J
The sack does not move up or down, so no work is done against gravity (the distance moved in the direction of the upward force is zero).
Common mistake10 000 J multiplies the weight (200 N) by the horizontal distance, but the weight acts vertically, not along the road.
32Short answer
State the main energy change in (a) a radio playing from batteries, (b) a microphone, (c) a person climbing Mount Kigali.
Show answer
Model answer: (a) Chemical → electrical → sound (and some heat). (b) Sound → electrical. (c) Chemical (food) → kinetic and gravitational potential energy (and heat).
Common mistakeLearners mix up a microphone and a loudspeaker; the microphone turns sound INTO electrical energy.
33Short answer · ★ Challenge
A goalkeeper claims that a 0.4 kg football kicked at 25 m/s has more than 100 J of kinetic energy. Check her claim with a calculation.
Show answer
Model answer: KE = ½ × 0.4 × 25² = ½ × 0.4 × 625 = 125 J. Her claim is correct: 125 J is more than 100 J.
Common mistakeLearners calculate ½ × 0.4 × 25 = 5 J and say she is wrong, forgetting to square the speed.
34Short answer
Name the main form of energy in: (a) water held behind a dam, (b) a bunch of bananas, (c) a moving moto, (d) a stretched bow.
Show answer
Model answer: (a) Gravitational potential energy. (b) Chemical energy. (c) Kinetic energy. (d) Elastic potential energy.
Common mistakeLearners give 'kinetic' for the dam water; it is not moving yet, so its energy is gravitational potential energy.
35Multiple choice
An electric motor takes in 800 J of electrical energy and gives out 600 J of useful kinetic energy. What is its efficiency?
1. A133%
2. B75%
3. C25%
4. D60%
Show answer
Answer: B. 75%
Efficiency = useful output ÷ total input × 100% = 600 ÷ 800 × 100% = 75%.
Common mistake133% comes from dividing input by output; efficiency can never be more than 100%.
36Multiple choice · ★ Challenge
How high must a 50 kg girl climb to gain 6000 J of gravitational potential energy (g = 10 N/kg)?
1. A120 m
2. B1.2 m
3. C12 m
4. D60 m
Show answer
Answer: C. 12 m
h = PE ÷ (mg) = 6000 ÷ (50 × 10) = 6000 ÷ 500 = 12 m.
Common mistake120 m comes from dividing by the mass only (6000 ÷ 50); you must divide by the weight, mg.
37Multiple choice
A cyclist and her bicycle (60 kg) move at 5 m/s. What is their kinetic energy?
1. A150 J
2. B750 J
3. C1500 J
4. D300 J
Show answer
Answer: B. 750 J
KE = ½mv² = ½ × 60 × 5² = ½ × 60 × 25 = 750 J.
Common mistake150 J comes from not squaring the speed (½ × 60 × 5).
38Multiple choice
Which is the best way for a school to cut its electricity bill?
1. ALeave computers on standby all night
2. BUse more filament bulbs in classrooms
3. CSwitch off lights and use LED bulbs
4. DOpen the fridge door more often
Show answer
Answer: C. Switch off lights and use LED bulbs
LEDs use much less power for the same light, and switching off saves energy completely.
Common mistakeStandby still uses some power all night; it does not save energy.
39Multiple choice · ★ Challenge
A builder weighing 600 N climbs a 15 m ladder. If his useful power is 300 W, how long does the climb take?
1. A30 s
2. B0.5 s
3. C20 s
4. D2 s
Show answer
Answer: A. 30 s
W = 600 × 15 = 9000 J; t = W ÷ P = 9000 ÷ 300 = 30 s.
Common mistake2 s comes from 600 ÷ 300, which leaves out the height climbed.
40Multiple choice
How much energy does a 2 kW iron use in 3 hours?
1. A1.5 kWh
2. B6000 kWh
3. C6 kWh
4. D5 kWh
Show answer
Answer: C. 6 kWh
E = Pt = 2 kW × 3 h = 6 kWh.
Common mistake6000 kWh comes from changing 2 kW into 2000 W, and 5 kWh from adding 2 + 3; with kWh multiply the power in kW by the time in hours.
41Multiple choice
A girl does 450 J of work pushing a cart with a steady force of 30 N in the direction it moves. How far does she push it?
1. A15 m
2. B13 500 m
3. C0.067 m
4. D420 m
Show answer
Answer: A. 15 m
d = W ÷ F = 450 ÷ 30 = 15 m.
Common mistake13 500 m comes from multiplying instead of dividing; distance = work ÷ force.
42Multiple choice · ★ Challenge
A 30 kg child slides from rest down a 2 m high slide and reaches the bottom at 5 m/s (g = 10 N/kg). How much energy is changed into heat by friction?
1. A375 J
2. B600 J
3. C225 J
4. D975 J
Show answer
Answer: C. 225 J
PE lost = 30 × 10 × 2 = 600 J; KE gained = ½ × 30 × 5² = 375 J; heat = 600 − 375 = 225 J.
Common mistake375 J is the kinetic energy at the bottom; the heat is the difference between PE lost and KE gained.
43Short answer
Box A (5 kg) is on a shelf 4 m high and box B (8 kg) is on a shelf 2 m high. Which box has more gravitational potential energy? Show your working (g = 10 N/kg).
Show answer
Model answer: PE of A = 5 × 10 × 4 = 200 J. PE of B = 8 × 10 × 2 = 160 J. Box A has more, even though it is lighter.
Common mistakeLearners choose B because it is heavier, ignoring the height.
44Short answer · ★ Challenge
A 0.3 kg mango falls 5 m from a tree. Ignoring air resistance, find its speed just before it reaches the ground (g = 10 N/kg).
Show answer
Model answer: PE lost = mgh = 0.3 × 10 × 5 = 15 J = KE gained. ½ × 0.3 × v² = 15, so v² = 100 and v = 10 m/s.
Common mistakeLearners forget to take the square root and give 100 m/s.
45Multiple choice
A water pump has a power of 750 W. How much energy does it transfer in 2 minutes?
1. A1500 J
2. B900 000 J
3. C90 000 J
4. D6.25 J
Show answer
Answer: C. 90 000 J
t = 2 × 60 = 120 s; E = Pt = 750 × 120 = 90 000 J.
Common mistake1500 J uses t = 2 instead of 120 s; the time must be in seconds (900 000 J is a slip of one zero).
46Short answer
A bucket of water weighing 120 N is pulled up a well 8 m deep at a steady speed. Find the work done on the bucket. Why is more work needed in total if the rope is heavy?
Show answer
Model answer: W = F × d = 120 × 8 = 960 J. A heavy rope must also be lifted, so extra work is done on the rope as well as on the bucket.
Common mistakeLearners use the mass instead of the weight; here the force (120 N) is already given.
47Short answer · ★ Challenge
A family replaces a 60 W filament bulb with a 10 W LED bulb that gives the same light. The bulb is on for 6 hours a day. How many kWh are saved in 30 days, and how much money at 200 FRW per kWh?
Show answer
Model answer: 60 W bulb: 0.06 × 6 × 30 = 10.8 kWh. LED: 0.01 × 6 × 30 = 1.8 kWh. Saved = 10.8 − 1.8 = 9 kWh, worth 9 × 200 = 1800 FRW.
Common mistakeLearners forget to change watts to kilowatts and get numbers 1000 times too big.
48Multiple choice
A 3 kg jerrycan of water is lifted from the floor onto a table 1.2 m high (g = 10 N/kg). How much gravitational potential energy does it gain?
1. A36 J
2. B3.6 J
3. C360 J
4. D4.2 J
Show answer
Answer: A. 36 J
PE = mgh = 3 × 10 × 1.2 = 36 J.
Common mistake3.6 J forgets to multiply by g; mass × height is not an energy.
49Short answer · ★ Challenge
An electric kettle is supplied with 200 000 J and the water gains 150 000 J. Find the efficiency, say where the rest of the energy goes and suggest one way to make the kettle more efficient.
Show answer
Model answer: Efficiency = 150 000 ÷ 200 000 × 100% = 75%. The other 50 000 J heats the kettle body and the surrounding air (and some sound). Insulating the kettle's walls (or using a lid) reduces the heat lost.
Common mistakeLearners say the missing energy is destroyed; it goes as heat into the surroundings.
50Short answer
Express 2.5 kW in watts and find how much energy a 2.5 kW electric water heater uses in 10 minutes.
Show answer
Model answer: 2.5 kW = 2.5 × 1000 = 2500 W. t = 10 × 60 = 600 s. E = Pt = 2500 × 600 = 1 500 000 J (1.5 MJ).
Common mistakeLearners multiply 2.5 by 10 and get 25 J, forgetting to convert kW to W and minutes to seconds.