Senior 2 practice book · Unit 6 of 10

Conservation of Mechanical Energy

50 questions that complete the Senior 2 quiz for this unit: 26 core and 24 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A body at the top of its path has no energy because it has stopped moving.It has no kinetic energy at that instant, but its potential energy is at its largest; the total mechanical energy is unchanged.
Doubling the speed of a car doubles its kinetic energy, so it needs twice the distance to stop.KE = ½mv², so doubling the speed makes the KE four times as large; with the same braking force the stopping distance is four times as long.
Friction destroys energy.Friction changes mechanical energy into heat (and sound). The total energy is conserved; only the useful mechanical energy decreases.
Potential energy has one true value for a body.PE = mgh depends on the reference level chosen for h; only CHANGES in PE matter, and they are the same whatever level is chosen.
A heavier body always gains more speed when it falls.Both PE (mgh) and KE (½mv²) are proportional to mass, so the mass cancels: without air resistance every body falling through h reaches v = √(2gh).

What this unit covers

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

Open, closed and isolated systems
Kinetic energy: KE = ½mv² and how it depends on mass and speed
Gravitational potential energy: PE = mgh and the reference level
Elastic potential energy stored in springs and catapults
Mechanical energy and the principle of its conservation
Falling and vertically thrown bodies: v = √(2gh) and h = v²/2g
Energy changes of pendulums, swings, slides and roller coasters
Energy dissipated by friction and air resistance
Work–energy relation: work done by a force = change in kinetic energy (stopping distances, average forces)
Rate of energy conversion: power and efficiency in lifting and hydroelectric problems
Energy–height and energy–time graphs
Experiments to check the conservation of mechanical energy (ramp, light gate, pendulum)

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 24 harder ones are marked ★ Challenge.

1True or false
In a real system with friction, the total energy of all forms together is still conserved.
Show answer
Answer: True
Mechanical energy decreases, but the heat and sound produced make up exactly the amount lost, so total energy is conserved.
Common mistakeLearners mix up 'mechanical energy conserved' (only without friction) with 'total energy conserved' (always true).
2True or false · ★ Challenge
A box pushed at constant speed across a rough floor gains kinetic energy from the work done by the push.
Show answer
Answer: False
At constant speed KE does not change; the push and friction are balanced, and the work done by the push becomes heat.
Common mistakeLearners think every push increases KE, but only the RESULTANT force changes KE, and here it is zero.
3True or false
When a minibus brakes to a stop, most of its kinetic energy is changed into heat in the brakes.
Show answer
Answer: True
Friction between the brake pads and the discs or drums changes KE into heat (with a little sound).
Common mistakeSome think the energy is simply destroyed when the bus stops, but it appears as heat in the brakes.
4True or false · ★ Challenge
If the compression of a spring is doubled, the elastic energy stored in it doubles.
Show answer
Answer: False
E = ½ke², so doubling e makes the energy 2² = 4 times as large.
Common mistakeLearners treat energy like force (F = ke doubles), but the energy depends on the square of the compression.
5True or false
A body moving backwards (with a negative velocity) has negative kinetic energy.
Show answer
Answer: False
KE = ½mv²; v² is positive whatever the direction, so KE is never negative.
Common mistakeLearners carry the sign of velocity into KE, but squaring removes the sign: energy has no direction.
6True or false · ★ Challenge
A ball thrown straight up at 10 m/s on the Moon (g = 1.6 m/s²) rises to the same height as on Earth.
Show answer
Answer: False
h = v²/2g: on Earth 100 ÷ 20 = 5 m; on the Moon 100 ÷ 3.2 ≈ 31 m. A smaller g means a greater height.
Common mistakeSome think the same throw gives the same height everywhere, but the height depends on g as well as on the speed.
7Fill in the blank
The energy stored in a stretched or compressed spring is called ______ potential energy.
Show answer
Answer: elastic
A deformed spring stores elastic (strain) potential energy that is released when it springs back.
Common mistakeWriting 'gravitational' confuses energy due to height with energy due to deformation.
8Multiple choice · ★ Challenge
The speed of a freely falling stone rises steadily with time. How does its kinetic energy change with time?
1. AIt rises steadily (KE ∝ t)
2. BIt rises faster and faster (KE ∝ t²)
3. CIt rises more and more slowly
4. DIt stays the same all the time
Show answer
Answer: B. It rises faster and faster (KE ∝ t²)
v = gt, so KE = ½m(gt)² ∝ t²: the KE rises faster and faster (its graph against time is a curve that gets steeper).
Common mistake'It rises steadily' is tempting because speed rises steadily with time, but KE depends on speed SQUARED.
9Fill in the blank
When a tight lid is put on a pot so that no steam can escape but heat still passes through its walls, the pot becomes a ______ system.
Show answer
Answer: closed
Energy (heat) can still cross the boundary but matter cannot, which defines a closed system.
Common mistakeWriting 'isolated' ignores the heat that still flows through the metal walls.
10Multiple choice · ★ Challenge
Four bodies are moving along a road in Musanze. Which one carries the most kinetic energy?
1. AA 150 kg moto (with rider) at 15 m/s
2. BA 0.4 kg football at 30 m/s
3. CA 60 kg runner at 8 m/s
4. DA 1200 kg car at 5 m/s
Show answer
Answer: A. A 150 kg moto (with rider) at 15 m/s
KE = ½mv²: moto ½ × 150 × 15² = 16 875 J; car ½ × 1200 × 5² = 15 000 J; runner 1920 J; football 180 J.
Common mistakeChoosing the car comes from looking only at mass; speed is squared, so the faster moto has more KE.
11Multiple choice
Which of these stores ELASTIC potential energy?
1. AA bucket of water on a high shelf
2. BA stretched catapult rubber
3. CA charged phone battery
4. DA hot flat iron
Show answer
Answer: B. A stretched catapult rubber
Elastic PE is stored when a material is stretched, squashed or bent and can spring back, as in a stretched catapult rubber.
Common mistakeThe bucket on the shelf stores gravitational PE, not elastic PE; both are 'potential' but their causes differ.
12Multiple choice · ★ Challenge
A student writes: 'At the top of its path, a ball thrown straight up has zero energy, because it has stopped.' What is wrong with this?
1. ANothing: a body at rest has no energy at all
2. BIts KE is greatest at the top of the path
3. CIts KE is zero there, but its PE is at its largest
4. DIts PE is zero at the top of the path
Show answer
Answer: C. Its KE is zero there, but its PE is at its largest
At the top v = 0, so KE = 0, but the ball is at its greatest height, so PE = mgh is largest and KE + PE is unchanged.
Common mistakeChoosing 'nothing is wrong' confuses 'no kinetic energy' with 'no energy'; PE is still stored.
13Multiple choice
In which situation is the mechanical energy of the moving body NOT conserved?
1. AA moto braking to a stop on a level road
2. BA ball rolling on a perfectly smooth track
3. CA stone falling in a vacuum
4. DA pendulum swinging with no air resistance
Show answer
Answer: A. A moto braking to a stop on a level road
Braking uses friction, which changes the moto's KE into heat, so KE + PE falls; the other cases have no friction.
Common mistakeSome think mechanical energy is conserved whenever there is motion; it is conserved only if no friction or other losses act.
14Multiple choice · ★ Challenge
The kinetic energy of a lorry rises from 100 kJ to 400 kJ. By what factor has its speed changed?
1. AIt has become 1.4 times as large
2. BIt has become 4 times as large
3. CIt has become 16 times as large
4. DIt has doubled
Show answer
Answer: D. It has doubled
KE ∝ v², so v ∝ √KE: √(400 ÷ 100) = √4 = 2.
Common mistakeAnswering 4 times assumes KE is proportional to v; because v is squared, 4 times the KE needs only twice the speed.
15Multiple choice
A trolley rolls down a ramp. Which change would reduce the energy changed into heat?
1. AUsing a heavier trolley
2. BMaking the ramp surface rougher
3. CReleasing it from higher up
4. DOiling the wheel axles
Show answer
Answer: D. Oiling the wheel axles
Oiling the axles reduces friction, so less mechanical energy is changed into heat.
Common mistakeA heavier trolley does not reduce friction losses; heavier objects press harder and often lose more energy.
16Multiple choice · ★ Challenge
A roller-coaster car starts from rest on a hill 30 m high. The track then goes over hill P (35 m high), hill Q (25 m) and hill R (10 m). With no friction, which hill can the car NOT get over?
1. AHill Q (25 m)
2. BNone, if the car is heavy enough
3. CHill R (10 m)
4. DHill P (35 m)
Show answer
Answer: D. Hill P (35 m)
Starting from rest at 30 m, the car's mechanical energy equals mg × 30, so it can never rise above 30 m: hill P (35 m) is too high.
Common mistakeChoosing 'none, if heavy enough' forgets that mass cancels: no car starting from rest can rise above its starting height.
17Fill in the blank
In a light-gate experiment, the speed of a trolley = length of the card ÷ the ______ for which the card blocks the beam.
Show answer
Answer: time
The timer measures how long the beam is cut; speed = distance (card length) ÷ time.
Common mistakeUsing the time for the whole run down the ramp gives the average speed, not the speed at the gate.
18Fill in the blank · ★ Challenge
A stone thrown vertically downwards at 5 m/s from a bridge hits the river at 15 m/s (g = 10 m/s², no air resistance). The bridge is ______ m above the water.
Show answer
Answer: 10
Gain in KE per kg = PE lost per kg: ½(15² − 5²) = 10h, so h = (225 − 25) ÷ 20 = 10 m.
Common mistakeUsing only the final speed (225 ÷ 20 = 11.25 m) forgets that the stone already had KE when it was thrown.
19Fill in the blank
The work done by the resultant force on a body equals the change in its ______ energy.
Show answer
Answer: kinetic
This is the work–energy relation: W = ΔKE = ½mv² − ½mu².
Common mistakeWriting 'potential' confuses the work of the resultant force with work done lifting a body.
20Multiple choice
A pot of beans boils on a charcoal stove with no lid. Steam escapes into the kitchen and heat passes through the pot walls. What type of system are the pot and its contents?
1. ANot a system, because it has no lid
2. BAn open system
3. CA closed system
4. DAn isolated system
Show answer
Answer: B. An open system
Both matter (steam) and energy (heat) leave the pot, so it is an open system.
Common mistakeChoosing 'closed' comes from thinking any container is closed; a closed system cannot lose matter, but here steam escapes.
21Short answer · ★ Challenge
Describe how you could use a pendulum, a metre rule and a light gate connected to a timer to check that mechanical energy is conserved.
Show answer
Model answer: Pull the bob aside and measure the height h of its centre above its lowest position with the metre rule. Release it from rest. Place the light gate at the lowest point; measure the bob's diameter and the time it blocks the beam, so speed v = diameter ÷ time. Compare ½v² with gh (per kilogram): if they are almost equal, mechanical energy is conserved. Repeat for several heights.
Common mistakeA frequent error is to measure the length of the string or the sideways distance instead of the vertical height h.
22Fill in the blank
If the floor is chosen as the reference level, a ball lying on the floor has a gravitational potential energy of ______ J.
Show answer
Answer: 0
PE = mgh with h = 0 at the reference level, so PE = 0 J.
Common mistakeLearners think every body must have some PE, but PE is measured from a chosen zero level.
23Multiple choice · ★ Challenge
A girl tosses a tennis ball straight up from ground level at 20 m/s. Taking the ground as zero PE and ignoring air resistance, at what height does the ball have equal amounts of kinetic and potential energy? (g = 10 m/s²)
1. A10 m
2. B20 m
3. C5 m
4. D14 m
Show answer
Answer: A. 10 m
Maximum height = v²/2g = 400 ÷ 20 = 20 m. KE = PE when each is half the total, i.e. at half the maximum height: 10 m.
Common mistake20 m is the maximum height, where KE = 0, not where KE = PE.
24Fill in the blank · ★ Challenge
A 2 kg stone is dropped from 5.0 m and hits the ground at 9.0 m/s (g = 10 m/s²). The energy changed into heat by air resistance is ______ J.
Show answer
Answer: 19
PE at top = 2 × 10 × 5 = 100 J; KE at bottom = ½ × 2 × 9² = 81 J; heat = 100 − 81 = 19 J.
Common mistakeLearners often forget the ½ in KE (giving 162 J, more than the starting PE), which is impossible.
25Fill in the blank
A goat running at 6 m/s has 540 J of kinetic energy. Its mass is ______ kg.
Show answer
Answer: 30
m = 2KE ÷ v² = 2 × 540 ÷ 6² = 1080 ÷ 36 = 30 kg.
Common mistakeForgetting the ½ in KE = ½mv² gives 15 kg, half the correct mass.
26True or false
A sealed bottle of cold soda left on a table in the sun is a closed system.
Show answer
Answer: True
No matter enters or leaves the sealed bottle, but heat from the sun and air flows in, so it is closed (not isolated).
Common mistakeMany learners think 'sealed' means isolated, but a sealed bottle still exchanges heat with its surroundings.
27Multiple choice · ★ Challenge
A trolley carrying a 5.0 cm card is released from rest 0.25 m (vertically) above the bottom of a ramp. At the bottom the card blocks a light gate for 0.025 s. What percentage of its PE has become KE? (g = 10 m/s²)
1. A50 %
2. B89 %
3. C20 %
4. D80 %
Show answer
Answer: D. 80 %
v = 0.050 ÷ 0.025 = 2.0 m/s. Per kg: KE = ½ × 2.0² = 2.0 J, PE = 10 × 0.25 = 2.5 J; 2.0 ÷ 2.5 × 100 % = 80 %.
Common mistake89 % compares speeds (2.0 ÷ 2.24) instead of energies; energy depends on v², so speeds cannot be compared directly.
28Multiple choice
A resultant force of 20 N pushes a 4 kg trolley from rest along 5 m of smooth floor. What is its final kinetic energy?
1. A25 J
2. B400 J
3. C100 J
4. D50 J
Show answer
Answer: C. 100 J
Work done = Fd = 20 × 5 = 100 J, and all of it becomes KE because the floor is smooth.
Common mistake25 J comes from multiplying the acceleration (5 m/s²) by the distance instead of the force by the distance.
29Multiple choice · ★ Challenge
A ball dropped from 2.0 m bounces back to 1.5 m. If each bounce keeps the same FRACTION of the energy, how high does it rise after the second bounce?
1. A0.75 m
2. B1.1 m
3. C1.0 m
4. D1.5 m
Show answer
Answer: B. 1.1 m
Each bounce keeps 1.5 ÷ 2.0 = 0.75 of the energy, so the second height = 0.75 × 1.5 ≈ 1.1 m (1.125 m).
Common mistake1.0 m comes from subtracting the same 0.5 m again; the loss is a fixed fraction, so it gets smaller each bounce.
30Short answer
Explain why we say energy is 'lost' to friction, even though the law of conservation of energy says energy cannot be destroyed.
Show answer
Model answer: Friction changes mechanical energy (KE + PE) into heat and sound, which spread out into the surroundings and cannot easily be used again. The TOTAL energy is unchanged; only the useful mechanical energy decreases, which is what 'lost' means here.
Common mistakeThe error is to think 'lost' means destroyed; it means changed into forms we cannot use.
31Multiple choice · ★ Challenge
A spring with spring constant 200 N/m is compressed by 0.1 m. How much elastic potential energy does it store? (E = ½ke²)
1. A2 J
2. B1 J
3. C20 J
4. D10 J
Show answer
Answer: B. 1 J
E = ½ke² = ½ × 200 × 0.1² = ½ × 200 × 0.01 = 1 J.
Common mistake10 J comes from forgetting to square the compression (½ × 200 × 0.1); 2 J forgets the ½.
32Short answer
A skateboarder starts from rest at the top of one side of a smooth U-shaped ramp, rolls down and up the other side. Describe the energy changes, and state where her speed is greatest.
Show answer
Model answer: At the top she has maximum PE and no KE. Going down, PE changes into KE, so she speeds up. At the bottom PE is least and KE (and speed) is greatest. Going up the other side, KE changes back into PE and she slows down, stopping at the same height she started from (no friction).
Common mistakeA frequent error is to say she is fastest halfway down; the speed is greatest at the LOWEST point, where most PE has become KE.
33Short answer · ★ Challenge
A hydroelectric station must produce 1.0 MW of electrical power. The water falls 60 m and the station is 85 % efficient (g = 10 m/s²). What mass of water must fall each second?
Show answer
Model answer: Useful power needed = 1.0 × 10⁶ W, so input power = 1.0 × 10⁶ ÷ 0.85 ≈ 1.18 × 10⁶ W. PE lost per second = mgh, so m = 1.18 × 10⁶ ÷ (10 × 60) ≈ 1960 kg (about 2000 kg) each second.
Common mistakeMultiplying by 0.85 instead of dividing gives too little water; the input must be LARGER than the output.
34True or false
On a graph of gravitational PE against height for a body near the Earth's surface, the gradient is equal to the weight mg of the body.
Show answer
Answer: True
PE = mgh, so PE ÷ h = mg: the gradient of the straight line is the weight (in N).
Common mistakeSome say the gradient is the mass; it is the mass times g, which is the weight.
35Short answer · ★ Challenge
On a smooth track, a 0.5 kg trolley passes point X, 1.8 m above the ground, at 4 m/s. What is the greatest height above the ground that the trolley can reach? (g = 10 m/s²)
Show answer
Model answer: At its highest point all its KE has become PE. Extra height = v²/2g = 4² ÷ 20 = 0.8 m. Greatest height = 1.8 + 0.8 = 2.6 m (the mass is not needed).
Common mistakeAnswering 0.8 m forgets that the trolley was already 1.8 m above the ground at X.
36Multiple choice
A crane lifts a 300 kg load of bricks 20 m in 30 s at a steady speed. What useful power does it develop? (g = 10 N/kg)
1. A2000 W
2. B60 000 W
3. C1 800 000 W
4. D200 W
Show answer
Answer: A. 2000 W
Gain in PE = mgh = 300 × 10 × 20 = 60 000 J; P = E ÷ t = 60 000 ÷ 30 = 2000 W.
Common mistake60 000 W forgets to divide by the time; 200 W forgets g, using mass instead of weight.
37Short answer · ★ Challenge
A pendulum in a school laboratory is released and left to swing. Describe the shape of a graph of its total mechanical energy against time, and explain it.
Show answer
Model answer: The graph starts at the initial PE and slowly falls towards zero, dropping a little with every swing (a decreasing curve, not a horizontal line). Air resistance and friction at the pivot change some mechanical energy into heat on each swing, so the total mechanical energy decreases until the pendulum stops.
Common mistakeDrawing a horizontal line describes an ideal pendulum; a real one always loses mechanical energy.
38Fill in the blank
A machine converts 600 J of electrical energy into 450 J of useful potential energy. Its efficiency is ______ %.
Show answer
Answer: 75
Efficiency = useful output ÷ input × 100 % = 450 ÷ 600 × 100 % = 75 %.
Common mistakeDividing input by output (600 ÷ 450) gives more than 100 %, which is impossible.
39Multiple choice · ★ Challenge
A car travelling at 10 m/s stops in 8 m when the brakes are applied. With the same braking force, how far will it take to stop from 20 m/s?
1. A24 m
2. B64 m
3. C32 m
4. D16 m
Show answer
Answer: C. 32 m
Work done by brakes = KE, so F × d = ½mv² and d ∝ v². Doubling v makes d 2² = 4 times: 4 × 8 = 32 m.
Common mistake16 m assumes stopping distance is proportional to speed; it depends on v², because KE does.
40Multiple choice
A stone falls from rest with no air resistance. What does a graph of its kinetic energy against the DISTANCE it has fallen look like?
1. AA curve that gets steeper and steeper
2. BA horizontal straight line
3. CA straight line sloping downwards
4. DA straight line through the origin
Show answer
Answer: D. A straight line through the origin
KE gained = PE lost = mg × distance fallen, so KE ∝ distance: a straight line through the origin with gradient mg.
Common mistakeChoosing the steepening curve mixes up distance with time; KE against time is curved, but KE against distance is straight.
41Short answer · ★ Challenge
A learner says: 'The Earth is an isolated system because almost no matter enters or leaves it.' Evaluate this statement.
Show answer
Model answer: The statement is wrong. The Earth receives a huge amount of energy from the Sun and radiates energy into space, so it exchanges energy with its surroundings. Since very little matter crosses its boundary, the Earth is best described as (approximately) a closed system, not an isolated one.
Common mistakeThe usual error is to look only at matter; a system is isolated only if it exchanges neither matter nor energy.
42Multiple choice
A child on a swing moves at 4 m/s at the lowest point. Ignoring air resistance, how high above the lowest point does she rise? (g = 10 m/s²)
1. A0.8 m
2. B0.4 m
3. C8.0 m
4. D1.6 m
Show answer
Answer: A. 0.8 m
½mv² = mgh, so h = v²/2g = 16 ÷ 20 = 0.8 m.
Common mistake8.0 m comes from v²/2 without dividing by g; 1.6 m forgets the 2 in 2g.
43Multiple choice · ★ Challenge
A 50 W electric motor is 80 % efficient. How long does it take to lift a 2 kg mass through 5 m? (g = 10 N/kg)
1. A1.6 s
2. B0.4 s
3. C2.5 s
4. D2.0 s
Show answer
Answer: C. 2.5 s
Useful energy = mgh = 2 × 10 × 5 = 100 J; input energy = 100 ÷ 0.80 = 125 J; t = 125 ÷ 50 = 2.5 s.
Common mistake2.0 s ignores the efficiency; 1.6 s multiplies by 0.80 instead of dividing, as if the motor were better than perfect.
44Multiple choice
A 50 kg learner climbs the stairs from the ground floor to the third floor of her school, a height of 9 m. How much gravitational PE does she gain? (g = 10 N/kg)
1. A13 500 J
2. B1500 J
3. C4500 J
4. D450 J
Show answer
Answer: C. 4500 J
ΔPE = mgh = 50 × 10 × 9 = 4500 J.
Common mistake450 J forgets to multiply by g; 13 500 J multiplies by 3 floors although the 9 m is already the total height.
45Short answer · ★ Challenge
Water in a tank on the roof of a Kigali building is 12 m above a tap on the ground floor. Another tap is on the third floor, 9 m above the ground. Use energy ideas to explain why water comes out faster from the ground-floor tap, and estimate both speeds, ignoring friction (g = 10 m/s²).
Show answer
Model answer: Water reaching the ground-floor tap has fallen 12 m, but water reaching the third-floor tap has fallen only 12 − 9 = 3 m. Each kilogram loses more PE (mgh) on the longer drop, so it gains more KE and comes out faster. v = √(2gh): ground floor √(2 × 10 × 12) ≈ 15 m/s; third floor √(2 × 10 × 3) ≈ 7.7 m/s.
Common mistakeA common slip is to use 9 m for the third-floor tap; the energy depends on the height FALLEN from the tank, which is 3 m.
46Multiple choice
A ripe mango falls from a branch and hits the ground at 6 m/s. Ignoring air resistance, how high was the branch? (g = 10 m/s²)
1. A1.8 m
2. B0.6 m
3. C3.6 m
4. D0.3 m
Show answer
Answer: A. 1.8 m
mgh = ½mv², so h = v² ÷ 2g = 6² ÷ (2 × 10) = 36 ÷ 20 = 1.8 m.
Common mistake3.6 m comes from forgetting the 2 in h = v²/2g; 0.6 m divides v (not v²) by g.
47Short answer · ★ Challenge
A 0.02 kg bullet travelling at 300 m/s enters a tree trunk and stops after 0.15 m. Find the average resisting force of the wood.
Show answer
Model answer: KE = ½mv² = ½ × 0.02 × 300² = 900 J. Work done by the wood = KE, so F × 0.15 = 900 and F = 900 ÷ 0.15 = 6000 N.
Common mistakeForgetting to square the speed gives 3 J of KE and a force of only 20 N, far too small to stop a bullet.
48Short answer
State two precautions that improve the accuracy of an experiment that checks conservation of energy with a trolley rolling down a ramp.
Show answer
Model answer: Any two: measure the VERTICAL height of the start above the bottom, not the length of the ramp; release the trolley from rest without pushing; reduce friction (smooth track, oiled wheels); make sure the card passes squarely through the light gate; repeat each reading and take an average.
Common mistakeLearners often measure the length along the slope, but PE depends on the vertical height.
49Multiple choice
A 2 kg cooking pot sits on a shelf 1.5 m above a table top. The table top is 0.8 m above the floor. What is the PE of the pot relative to the TABLE TOP? (g = 10 N/kg)
1. A3 J
2. B30 J
3. C16 J
4. D46 J
Show answer
Answer: B. 30 J
Relative to the table top h = 1.5 m, so PE = mgh = 2 × 10 × 1.5 = 30 J.
Common mistake46 J uses the height above the floor (2.3 m); PE must be measured from the reference level the question names.
50Short answer · ★ Challenge
A catapult rubber is pulled back 0.20 m; the force needed rises steadily from 0 to 30 N. The elastic energy stored is ½Fe. All of it is given to a 0.05 kg stone. Find the speed of the stone as it leaves the catapult.
Show answer
Model answer: E = ½Fe = ½ × 30 × 0.20 = 3 J. KE = ½mv², so v = √(2E ÷ m) = √(2 × 3 ÷ 0.05) = √120 ≈ 11 m/s.
Common mistakeUsing E = Fe (6 J) forgets that the force grew from 0 to 30 N, so the average force is only 15 N.