A.3 Work, energy and power
Practice exam-style IB Physics questions for Work, energy and power, aligned with the syllabus and grouped by topic.
Question 1
A system is isolated. What is conserved for the system?
A.
Power output
B.
Total energy
C.
Useful energy only
D.
Kinetic energy only
Question 2
A force of 50 N acts on a box through a displacement of 4.0 m. The force is at 60° to the displacement. What is the work done by the force?
A.
170 J
B.
800 J
C.
100 J
D.
200 J
Question 3
A satellite moves at constant speed in a circular orbit. The gravitational force provides the centripetal force. What is the work done by the gravitational force during one complete orbit?
A.
Positive and equal to the gravitational potential energy
B.
Zero
C.
Negative and equal to the loss of kinetic energy
D.
Positive and equal to the gain in kinetic energy
Question 4
A 0.60 kg ball is raised vertically through 1.5 m. Take g = 9.8 N kg⁻¹. What is the increase in gravitational potential energy?
A.
8.8 J
B.
5.9 J
C.
15 J
D.
0.90 J
Question 5
A motor transfers 2.4 kJ of useful energy in 12 s. What is its useful output power?
A.
200 W
B.
29 kW
C.
20 W
D.
0.20 W
Question 6
A student pulls a suitcase with a force of 35 N at an angle of 40° above the horizontal. The suitcase moves 6.0 m horizontally.
State the equation for work done by a constant force at an angle to the displacement.
[1]
Calculate the work done by the pulling force on the suitcase.
[1]
Question 7
A spring obeys Hooke’s law. A force of 12 N produces an extension of 0.080 m.
Calculate the spring constant.
[1]
Calculate the elastic potential energy stored at this extension.
[1]
Question 8
A Sankey diagram is used to represent the energy transfers in a lamp.
State what the width of an arrow represents in a Sankey diagram.
[1]
Outline why the total width of arrows leaving a junction must equal the width entering it.
[1]
Question 9
The speed of a trolley of mass 2.0 kg increases from 3.0 m s⁻¹ to 5.0 m s⁻¹. What is the increase in kinetic energy?
A.
4.0 J
B.
25 J
C.
34 J
D.
16 J
Question 10
A spring of spring constant 80 N m⁻¹ is compressed by 0.050 m. What is the elastic potential energy stored?
A.
8.0 J
B.
2.0 J
C.
4.0 J
D.
0.10 J
Question 11
A device has an input power of 500 W and a useful output power of 125 W. What is its efficiency?
A.
0.25
B.
0.40
C.
625
D.
4.0
Question 12
A generator requires 6.0 × 10⁸ J of input energy from a fuel. The fuel has energy density 3.0 × 10¹⁰ J m⁻³. What volume of fuel is required?
A.
1.8 × 10¹⁹ m³
B.
5.0 × 10¹ m³
C.
2.0 × 10⁻² m³
D.
5.0 × 10⁻³ m³
Question 13
A ball falls through air and reaches terminal speed. During terminal motion, what is true for the ball?
A.
Mechanical energy is conserved because the speed is constant.
B.
The work done by air resistance is zero.
C.
Gravitational potential energy is transformed only into kinetic energy.
D.
The loss of gravitational potential energy is transferred mainly to internal energy of the surroundings.
Question 14
A metal ball is dropped onto a hard floor and rebounds to a smaller height.
State the principle of conservation of energy.
[1]
Explain why the smaller rebound height does not contradict this principle.
[1]
Question 15
A 0.40 kg toy car starts from rest at the top of a frictionless track and descends through a vertical height of 0.75 m. Take g = 9.8 N kg⁻¹.
State the energy transfer that occurs as the car descends.
[1]
Calculate the speed of the car at the bottom of the track.
[1]
Question 16
A lift raises a 320 kg load through a height of 8.0 m in 20 s at constant speed. Take g = 9.8 N kg⁻¹.
Calculate the gain in gravitational potential energy of the load.
[1]
Calculate the useful power output of the lift motor.
[1]
Question 17
An electric motor has an input power of 900 W. It delivers 630 W of useful mechanical power.
Calculate the efficiency of the motor.
[1]
State one form of energy transfer that accounts for the remaining input power.
[1]
Question 18
The graph shows the horizontal force on a trolley as a function of displacement.
Estimate the work done by the force over the full displacement shown.
[1]
The trolley has mass 0.80 kg and starts from rest. Calculate its final speed, assuming no resistive forces.
[1]
Question 19
A Sankey diagram shows the energy transfers in a small electric motor.
Determine the useful energy output.
[1]
Calculate the efficiency of the motor.
[1]
Suggest one reason why the motor is not 100% efficient.
[1]
Question 20
The table gives drop height and rebound height for a rubber ball.
| Trial | Drop height / m | Rebound height / m |
|---|---|---|
| 1 | 0.30 | 0.19 |
| 2 | 0.50 | 0.31 |
| 3 | 0.70 | 0.44 |
| 4 | 0.90 | 0.56 |
| 5 | 1.10 | 0.67 |
| 6 | 1.30 | 0.78 |
Calculate the bounce efficiency for one trial using the table.
[1]
Describe how the data show whether the efficiency is constant over the range of drop heights.
[1]
Suggest one improvement to reduce random uncertainty in rebound height.
[1]
Question 21
A block is pulled along a horizontal surface by a 40 N force for 5.0 m. A frictional force of 12 N acts on the block. The pulling force is parallel to the motion. What is the change in kinetic energy of the block?
A.
260 J
B.
60 J
C.
140 J
D.
200 J
Question 22
A cyclist descends from rest through a vertical height of 20 m. Resistive forces do 1.2 kJ of work on the cyclist and bicycle. The total mass is 70 kg. Take g = 9.8 N kg⁻¹. What is the speed at the bottom?
A.
20 m s⁻¹
B.
18 m s⁻¹
C.
19 m s⁻¹
D.
36 m s⁻¹
Question 23
A vehicle engine delivers constant useful power to the wheels. Resistive forces are negligible. What happens to the acceleration as the speed increases?
A.
It decreases because the driving force decreases.
B.
It remains constant because the power is constant.
C.
It decreases because kinetic energy is conserved.
D.
It increases because the energy transferred each second increases.
Question 24
The extension of a spring that obeys Hooke’s law is increased from x to 3x. What is the additional elastic potential energy stored during this increase?
A.
k x²
B.
4k x²
C.
9k x²
D.
2k x²
Question 25
Two objects have the same momentum. Object X has mass m and object Y has mass 4m. What is the ratio kinetic energy of X : kinetic energy of Y?
A.
4 : 1
B.
1 : 2
C.
1 : 4
D.
2 : 1
Question 26
A pump lifts water at a rate of 0.020 m³ s⁻¹ through a height of 15 m. The density of water is 1000 kg m⁻³ and the input power is 4.0 kW. Take g = 9.8 N kg⁻¹. What is the efficiency of the pump?
A.
0.074
B.
0.74
C.
1.4
D.
2.9
Question 27
A 1.5 kg block moving at 6.0 m s⁻¹ slides along a rough horizontal surface and comes to rest.
Calculate the initial kinetic energy of the block.
[1]
Determine the work done by friction on the block.
[1]
Question 28
A 65 kg skier starts from rest and descends a slope. The vertical drop is 30 m. At the bottom the skier’s speed is 20 m s⁻¹. Take g = 9.8 N kg⁻¹.
Calculate the loss of gravitational potential energy.
[1]
Calculate the gain in kinetic energy.
[1]
Determine the work done by non-conservative forces on the skier.
[1]
Question 29
A portable heater has useful output power 1.8 kW and efficiency 0.60. It is powered by a liquid fuel of energy density 3.6 × 10¹⁰ J m⁻³.
Calculate the input power required from the fuel.
[1]
Calculate the volume of fuel used in 2.0 h.
[1]
Question 30
A pendulum bob moves along a circular arc. The tension in the string is directed towards the pivot.
State the angle between the tension and the instantaneous displacement of the bob.
[1]
Explain why the tension does no work on the bob.
[1]
Question 31
A ball is dropped from 1.60 m and rebounds to 0.90 m.
Calculate the efficiency of the bounce, treating the useful output as gravitational potential energy at rebound height.
[1]
State two assumptions made in using the ratio of heights for the efficiency.
[1]
Question 32
A student measures the force needed to extend a spring. The graph shows force against extension.
State how the spring constant can be obtained from the graph.
[1]
Determine the spring constant from the graph.
[1]
Estimate the elastic potential energy stored at the largest extension shown.
[1]
Question 33
A cart is released from different heights on a track. The graph shows the measured speed at the bottom as a function of release height.
State the expected relationship between v² and h if mechanical energy is conserved.
[1]
Use the graph to determine whether the data are consistent with this relationship.
[1]
Suggest one cause of any systematic difference between the measured speeds and ideal predictions.
[1]
Question 34
A car of mass 900 kg travels at 24 m s⁻¹ on a level road. The useful power at the wheels is 18 kW and the total resistive force is 600 N.
Calculate the driving force provided by the wheels at this speed.
[1]
Determine whether the car is accelerating at this instant.
[1]
Question 35
A particle has momentum 12 kg m s⁻¹ and mass 3.0 kg.
Calculate its kinetic energy using momentum.
[1]
The momentum is doubled while the mass remains constant. Determine the new kinetic energy.
[1]
Question 36
In an experiment a cart is pulled by a falling mass. The measured decrease in gravitational potential energy of the falling mass is greater than the measured increase in translational kinetic energy of the cart and falling mass.
Suggest one physical reason for this difference.
[1]
Suggest two experimental improvements that would help test energy conservation more reliably.
[1]
Question 37
A force acting on a cart varies with displacement. The force increases uniformly from 0 N to 20 N over the first 0.50 m, then remains at 20 N for the next 0.30 m.
State how work done is found from a force–displacement graph.
[1]
Determine the total work done by the force over the 0.80 m displacement.
[1]
Question 38
A battery-powered cart is tested on a horizontal track. The graph shows useful driving power and power dissipated by resistive forces as functions of speed.
State the condition for the cart to travel at constant maximum speed.
[1]
Determine the maximum speed from the graph.
[1]
Explain how the acceleration changes as the cart approaches this speed.
[1]
Suggest why the maximum speed would be lower on a rougher track.
[1]
Question 39
The table compares several fuels used for heating.
| Fuel | Energy density / J m^-3 | Efficiency / % |
|---|---|---|
| Natural gas | 3.9 × 10^7 | 90 |
| LPG (liquid) | 2.5 × 10^10 | 85 |
| Heating oil | 3.6 × 10^10 | 88 |
| Ethanol | 2.1 × 10^10 | 70 |
| Wood pellets | 1.0 × 10^10 | 80 |
Identify the fuel requiring the smallest volume to provide the same input energy.
[1]
Calculate the volume of one fuel required to deliver a specified useful energy, using its efficiency.
[1]
Discuss one limitation of choosing a fuel using energy density alone.
[1]
Question 40
A student tests conservation of mechanical energy for a glider pulled by a falling mass. The table shows gravitational potential energy lost and kinetic energy gained for repeated trials.
| Trial | GPE lost / J | Unc. in GPE / J | KE gained / J | Unc. in KE / J |
|---|---|---|---|---|
| 1 | 0.118 | ±0.006 | 0.112 | ±0.007 |
| 2 | 0.146 | ±0.007 | 0.138 | ±0.008 |
| 3 | 0.173 | ±0.008 | 0.164 | ±0.009 |
| 4 | 0.201 | ±0.009 | 0.190 | ±0.010 |
| 5 | 0.228 | ±0.010 | 0.216 | ±0.011 |
Calculate the energy difference for one trial.
[1]
Determine whether the results support conservation of total energy within experimental uncertainty.
[1]
Suggest two energy stores or transfers that should be included if mechanical energy is not conserved.
[1]
Question 41
A spring-launch experiment is used to find a spring constant. The graph shows maximum height reached by a small projectile against the square of the spring compression.
Explain why the graph is expected to be linear.
[1]
Determine the spring constant from the gradient of the graph.
[1]
Suggest one reason why the value may differ from a static force–extension measurement.
[1]
Question 42
A child slides from rest down a smooth curved slide of vertical height h and then along a rough horizontal surface until coming to rest.
Explain why the speed at the bottom of the smooth slide does not depend on the shape of the slide.
[1]
The rough horizontal surface exerts a constant frictional force. Explain how energy considerations can be used to determine the stopping distance on the horizontal surface.
[1]
Question 43
An electric kettle transfers energy from the mains supply to heat water. Some energy is transferred to the surroundings.
Define efficiency and state how it can be represented on a Sankey diagram.
[1]
Discuss how measurements could be used to determine the efficiency of the kettle when heating a known mass of water.
[1]
Question 44
A spring is compressed and used to launch a small cart along a horizontal track.
Derive the expression for the elastic potential energy stored in a spring that obeys Hooke’s law.
[1]
Explain how the launch speed of the cart depends on the compression of the spring, and describe the effect of friction.
[1]
Question 45
A cyclist moves along a straight road. The graph shows the resultant force on the cyclist as a function of distance over a short interval.
Determine the net work done over the interval.
[1]
The cyclist’s initial kinetic energy is given. Determine the final kinetic energy.
[1]
Explain the physical meaning of any section of the graph below the distance axis.
[1]
Question 46
A student claims that energy is not conserved when a moving clay ball collides with a wall and sticks to it, because the ball has no kinetic energy after the collision.
State the work–energy principle for the ball during the collision.
[1]
Evaluate the student’s claim, referring to system choice and energy transfers.
[1]
Question 47
A car engine can deliver a maximum constant useful power to the wheels. The car travels on a level road where resistive force increases with speed.
Explain why the driving force available from the engine decreases as the speed increases.
[1]
Evaluate how the motion changes from low speed until the car reaches its maximum speed.
[1]
Question 48
A remote research station must choose between two fuel sources. Fuel A has a higher energy density, while fuel B can be used in a device with higher efficiency.
Outline how to calculate the volume of fuel required to provide a specified useful energy output.
[1]
Discuss factors, in addition to energy density, that should influence the choice of fuel.
[1]
Question 49
Two routes lead from the same starting point to the same finishing point at a lower height. Route X is a smooth track. Route Y is a rough track of greater length.
Distinguish between conservative and non-conservative forces in terms of work done.
[1]
Compare the final speeds of identical carts released from rest on the two routes, using energy arguments.
[1]
Question 50
A group of students investigates a falling mass that pulls a cart along a track. They measure the loss of gravitational potential energy of the falling mass and the increase in translational kinetic energy of the cart and falling mass.
Explain why these two measured energy changes may not be equal even if total energy is conserved.
[1]
Evaluate how the investigation could be designed and analysed to test conservation of energy despite measurement uncertainty.
[1]
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