Kinetic, elastic and gravitational potential energy

Figure 7 shows a skier sliding down a slope.

The gravitational potential energy of the skier decreases by 39 000 J between the top and the bottom of the slope.

The mass of the skier is 70 kg.

Calculate the height, h, of the slope.

The value of g is 10 N / kg.

Use the equation

Δ GPE = m × g × h

The skier starts from rest at the top of the slope.

The velocity of the skier at the bottom of the slope is 27 m / s.

Using information from Figure 7, calculate the acceleration of the skier along the slope.

acceleration =_........ m / s²

When the skier slides from the top to the bottom of the slope, some energy is dissipated.

Explain how to determine the amount of energy dissipated.

Figure 8 shows athletes running at a constant speed on a curved section of

Even though they are running at a constant speed, the velocity of each athlete is changing.

State why the velocity of each athlete is changing.

The athletes start the race on a straight section of track.

Figure 9 shows a distance / time graph for one of the athletes.

Determine the gradient of this graph at a time of 2.5 s.

gradient =_........

Carbon-14 is a radioactive substance that emits beta minus (β^–) particles.

Which of these is the unit for the activity of a sample of carbon-14?

Which row of the table gives a correct comparison of the penetrating abilities of alpha, beta and gamma radiation?

The mass of a beta minus particle is 9.1 × 10^–31kg.

Calculate the kinetic energy of a beta minus particle moving with a speed of 3.8 × 10⁶m / s.

kinetic energy =_........

Describe what happens in the nucleus of an atom when a beta plus particle is emitted.

*(c) Radioactive decay can produce gamma radiation and alpha radiation.

Compare the processes of gamma decay and alpha decay.

Your answer should include

• a description of both gamma radiation and alpha radiation

• the effect of each type of decay on the original nucleus.

A student places a trolley at the top of a runway, as shown in Figure 9.

The student had to lift the trolley through a height of 26 cm to put it at the top of the runway.

The gravitational potential energy, Δ GPE, of the trolley increases by 4.1 J when lifted to the top of the runway.

The gravitational field strength, g, = 10 N / kg.

Show that the mass of the trolley is about 1.6 kg.

Use the equation

The student releases the trolley and the trolley moves down the runway.

The student assumes that all the extra gravitational potential energy, Δ GPE, stored at the top of the runway is transferred to kinetic energy at the end of the runway.

Calculate the expected value of the velocity of the trolley at the end of the runway.

Use the equation

expected velocity =_........

The light gate, shown in Figure 9, is used to determine the actual velocity of the trolley at the end of the runway.

The actual velocity at the end of the runway is less than the expected velocity as calculated in part (ii).

Suggest one way to reduce the difference between the actual velocity and the expected velocity.

A different student finds out how much power can be generated by running up some stairs in a measured amount of time.

The following quantities are measured:

mass of student = 48 kg

total height of stairs = 2.9 m

time to run up stairs = 3.4 s

Calculate the power the student generated.

Give the answer to 2 significant figures (2 s.f.).

Use the equation

Explain how the total height of the stairs can be found using a 50 cm ruler.

A student places a trolley at the top of a runway, as shown in Figure 1.

The student had to lift the trolley through a height of 26 cm to put it at the top of the runway.

The gravitational potential energy, Δ GPE, of the trolley increases by 4.1 J when lifted to the top of the runway.

The gravitational field strength, g, = 10 N / kg.

Show that the mass of the trolley is about 1.6 kg.

Use the equation

The student releases the trolley and the trolley moves down the runway.

The student assumes that all the extra gravitational potential energy, ∆ GPE, stored at the top of the runway is transferred to kinetic energy at the end of the runway.

Calculate the expected value of the velocity of the trolley at the end of the runway.

Use the equation

expected velocity =_........

The light gate, shown in Figure 1, is used to determine the actual velocity of the trolley at the end of the runway.

The actual velocity at the end of the runway is less than the expected velocity as calculated in (ii).

Suggest one way to reduce the difference between the actual velocity and the expected velocity.

A different student finds out how much power can be generated by running up some stairs in a measured amount of time.

The following quantities are measured:

mass of student = 48 kg

total height of stairs = 2.9 m

time to run up stairs = 3.4 s

Calculate the power the student generated.

Give the answer to 2 significant figures (2 s.f.).

Use the equation

Figure 9 shows a person on a skateboard at the top of a ramp.

At P, the person is not moving.

The person rides the skateboard down the ramp from P to Q.

The gravitational potential energy of the person decreases by 980 J.

The mass of the person is 35 kg.

Calculate h, the height of the ramp.

Use g = 10 N/kg.

Use the equation

change in gravitational potential energy = m g h

h =_........ m

The kinetic energy, KE, of the person at Q is 950 J.

The mass of the person is 35 kg.

Calculate the velocity of the person at Q.

Use the equation

velocity =_........ m/s

Figure 10 is a diagram that represents energy changes from P to Q.

State what is represented by X.

Calculate the value of X.

value of X =_........ J

Calculate the efficiency of the system represented in Figure 10.

efficiency =_........

The person would like to start from P again but have a greater velocity at Q.

Suggest two ways that this can be achieved.

Figure 1 shows a person on a skateboard at the top of a ramp.

At P, the person is not moving.

The person rides the skateboard down the ramp from P to Q.

The gravitational potential energy of the person decreases by 980 J.

The mass of the person is 35 kg.

Calculate h, the height of the ramp.

Use g = 10 N/kg.

Use the equation

change in gravitational potential energy = m g h

h =_........ m

The kinetic energy, KE, of the person at Q is 950 J.

The mass of the person is 35 kg.

Calculate the velocity of the person at Q.

Use the equation

velocity =_........ m/s

Figure 2 is a diagram that represents energy changes from P to Q.

State what is represented by X.

Calculate the value of X.

value of X =_........ J

Calculate the efficiency of the system represented in Figure 2.

efficiency =_........

Figure 5 shows a truck on a horizontal road.

A force of 1200 N pulls the truck along the road for a distance of 8.0 m.

Calculate the work done by the 1200 N force.

Use the equation

work done = force distance moved in the direction of the force

State the unit of work done.

work done =_........

unit_........

At 8.0 m the force is removed and the truck slows down until it stops.

Describe the energy transfers as the truck slows down.

A box has a mass of 90 kg.

Which of these is the weight of the box?

Figure 6 shows a truck lifting a different box.

A student calculates the change in gravitational potential energy, ΔGPE, for the box at different heights.

Figure 7 shows the results of the student’s calculations.

The student has made one incorrect calculation.

The truck lifts the box from the ground to a height of 2.0 m.

This takes a time of 5.0 s.

Using data from the graph in Figure 7, calculate the power needed to lift the box.

Use the equation

power =_........ W

Figure 8 shows an athlete training with a push sled.

The athlete pushes the sled with a force of 645 N.

Calculate the distance the sled moves when the force of 645 N does 7440 J of work on the sled.

Give your answer to an appropriate number of significant figures.

distance moved =_........ m

Figure 9 shows an electric motor lifting a set of masses.

Describe an experiment, using the apparatus in Figure 9, to determine the gravitational potential energy gained by the masses as they are lifted.

Your description should include any measuring devices to be used.

You may add to the diagram in Figure 9 if it helps your answer.

In one experiment, the change in gravitational potential energy of the masses was 5.8 J.

The total mass lifted was 320 g.

Calculate the vertical height the masses travelled through.

Use g = 10 N/kg.

height =_........ m

The efficiency of the motor was 59%.

State one reason why the motor was not 100% efficient.

Figure 10 shows a football kicked against a wall.

The football has a mass of 0.42 kg.

The football gains 11 J of gravitational potential energy as it moves from the ground to the wall.

Calculate the height at which the ball hits the wall.

Gravitational field strength = 10 N / kg

Use the equation

∆ GPE = m × g × ∆ h

height =_........ m

Calculate the kinetic energy of the football when it is moving at a velocity of 12 m / s.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the ball hits the wall.

*(b) In the UK, electricity is generated using non‑renewable and renewable energy resources.

The graph in Figure 11 shows how the amount of electricity generated by these resources changed from 2012 to 2020.

time in years from 2012 to 2020

Figure 11

Explain how and why the amount of electricity generated by renewable and non‑renewable energy resources has changed from 2012 to 2020.

Your answer should include

• the trends shown in Figure 11

• the change in the amount of electricity generated by at least one renewable resource

• the change in the amount of electricity generated by at least one non‑renewable resource.

Equations

Figure 4 shows a football kicked against a wall.

The football has a mass of 0.42 kg.

The football gains 11 J of gravitational potential energy as it moves from the ground to the wall.

Calculate the height at which the ball hits the wall.

Gravitational field strength = 10 N / kg

Use the equation

∆ GPE = m × g × ∆ h

height =_........ m

Calculate the kinetic energy of the football when it is moving at a velocity of 12 m / s.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the ball hits the wall.

A stone is held at rest above the ground.

The stone is released and falls until its velocity is 17 m / s.

Calculate the distance the stone has fallen when its velocity has reached 17 m / s.

distance =_........ m

This question is about energy transfers.

Figure 8 shows the apparatus used for investigating the transfer between gravitational potential energy and kinetic energy.

A metal ball is attached to a thread.

The ball is released from a starting position and swings on the thread.

The ball cuts a light beam at the bottom of its swing.

When the ball cuts the light beam, the speed of the ball is recorded by the data logger.

The ball was released 3 times from the same height and the speed measured each time.

The measurements of speed are given in Figure 9.

Calculate the mean speed.

mean speed =_........ m/s

Suggest one reason why the measurements of speed were repeated.

The mass of the ball is 0.052 kg.

The ball falls through a vertical height (Δ h) of 5.0 cm as it swings.

The gravitational field strength, g, is 10 N/kg.

Calculate the change in the gravitational potential energy of the ball.

Use the equation

change in gravitational potential energy =_........ J

Figure 10 shows an end‑on view of the ball’s swing from its starting position.

To measure the change in vertical height, Δ h, through which the ball moves, a ruler could be used.

Draw a ruler on Figure 10, placed in a position to measure the change in vertical height Δ h.

Figure 11 shows a set square.

Describe how the measurement of the change in vertical height, Δ h, could be improved using the set square.

You may add to Figure 10 or Figure 11 to help your description.

An electric car is travelling at a speed of 16.0 m/s.

The total mass of the car is 1200 kg.

Calculate the kinetic energy, in kJ, of the car.

kinetic energy =_........ kJ

On a journey, the car transfers energy from the battery at an average rate of 17.5 kW.

The battery in the car transfers a total of 126 MJ of energy before it becomes discharged.

Calculate the time taken for the battery to become discharged on this journey.

Give your answer in hours.

time taken =_........ hours

Figure 10 shows an electrical device connected to the wheels of an electric car.

dynamo when the car decelerates.

Explain how using the device can help to increase the time that the car can be driven before the battery becomes discharged.

The battery can be recharged at a charging point.

The charging point provides an average current of 15.0 A to the battery, at a potential difference (voltage) of 400 V.

It is claimed that 126 MJ of energy can be transferred to the battery in less than 6 hours.

Comment on this claim.

Use this equation to support your answer

Calculate the total charge that moves into the battery while it is being recharged.

Use the equation

charge =_........ C

Figure 4 shows a truck lifting a box.

The box has a mass of 57 kg.

The truck lifts the box through a vertical height of 2.1 m.

The gravitational field strength, g = 10 N/kg

Calculate the change in the gravitational potential energy of the box.

Use the equation

change in gravitational potential energy =_........ J

A cyclist of mass 70 kg travels at a constant velocity of 8 m/s.

Calculate the kinetic energy of the cyclist.

kinetic energy of the cyclist =_........ J

Figure 5 shows a trolley at the top of a slope.

A student gently pushes the trolley until it just starts to roll down the slope.

The student measures the time it takes for the trolley to roll down the slope.

The student repeats this for different values of the angle α.

Figure 6 is a graph of the student’s results.

Use the graph in Figure 6 to find the time the trolley takes to roll down the ramp when the angle α = 45.

time =_........ s

Use the graph in Figure 6 to estimate the time the trolley takes to roll down the ramp when the angle α = 80.

Show your working on the graph.

time =_........ s

The student had a choice of how to measure the time the trolley takes to roll down the ramp.

1. Use a hand‑held stopwatch.

2. Use light gates at the top and bottom of the slope.

The student chose to use the light gates.

Explain why this was the correct choice.

You should refer to the data on the time axis of Figure 6 in your answer.

An aircraft starts from rest and accelerates along the runway for 36 s to reach take‑off velocity.

Take‑off velocity for this aircraft is 82 m/s.

Show that the acceleration of the aircraft along the runway is about 2 m/s².

Assume the acceleration is constant.

Calculate the distance the aircraft travels along the runway before take‑off.

Use the equation

distance =_........ m

Suggest one reason why the length of the runway used is always much longer than the calculated distance that the aircraft travels along the runway before take-off.

The aircraft lands with a velocity of 71 m/s.

Calculate the kinetic energy of the aircraft as it lands.

kinetic energy of aircraft =_........ J

When the aircraft has come to a stop, all the kinetic energy has been transferred to the surroundings.

Give one way that the energy has been transferred to the surroundings.

Three students carry out an investigation to determine their powers when running up stairs.

Figure 7 shows a diagram of the stairs with four distances, A, B, C and D, marked.

The students need to calculate the work done against gravity.

Which distance should be used in the calculation?

They take turns to run up the stairs and use a stopwatch to measure the time taken.

The students estimate their own weight.

Figure 8 shows a table of their results.

The table is not complete.

State the unit for work done.

unit for work done is_........

Use the data for student B to calculate his estimated weight.

weight =_........ N

Use the data for student C to calculate the time she takes.

time taken =_........ s

Use the data for all three students to calculate the average power of the students.

average power =_........ W

Identify a significant source of error in the investigation and state how this error can be reduced.

source of error

can be reduced by

Calculate the change in gravitational potential energy of the rover as it descends from position P to position Q.

Mass of rover = 1100 kg

Gravitational field strength on Mars = 3.7 N / kg

Give your answer to 2 significant figures.

change in gravitational potential energy =_........ J

Use data from Figure 6 to calculate the change in kinetic energy of the rover as it descends from position P to position Q.

change in kinetic energy =_........ J

The rover is slowed down safely using thrusters and a parachute (not shown in Figure 6).

The thrusters use jets of gas to control movements and the parachute is designed to be used in the atmosphere of Mars.

Describe the energy changes involved in terms of the work done by various forces as the rover descends.

The rover uses solar panels for its power needs.

The solar panels can provide 1200 W of power.

Show that the solar panels can provide 2.16 MJ of energy in 30 minutes.

The solar panels convert 27% of the energy they receive from the Sun into electricity.

Calculate the solar energy received by the panels that provides the 2.16 MJ of energy.

energy received =_........ J

A cyclist has a mass of 64 kg.

The cyclist rides from a flat road to the top of a hill.

The top of the hill is 24 m above the flat road.

Calculate the gain in gravitational potential energy, ∆ GPE, of the cyclist.

Use g = 10 N/kg

Use the equation

gain in gravitational potential energy =_........ J

The cyclist returns to the flat road.

The mass of the cyclist is 64 kg.

Calculate the kinetic energy of the cyclist when the cyclist is travelling at 6.0 m/s.

Use the equation

kinetic energy =_........ J

The cyclist then uses the brakes on the bicycle to stop.

Explain what happens to the kinetic energy of the cyclist.

A different cyclist uses a motorised bicycle.

The motorised bicycle is powered by an electric motor.

Figure 3 is an energy diagram for the motor.

Calculate how much energy is wasted.

energy wasted =_........ J

Calculate the efficiency of the electric motor.

Use the equation:

efficiency of electric motor =_........

This question is about energy changes.

Figure 8 shows a water slide. A person travels from the top to the bottom of the water slide.

The mass of the person, m = 72 kg. The change in vertical height, h = 7.0 m Gravitational field strength, g = 10 N / kg

Calculate the change in gravitational potential energy for the person.

Use the equation

change in gravitational potential energy = m × g × h

change in gravitational potential energy =_........ J

The person comes to rest after the end of the water slide.

Explain what happens to the energy as the person comes to rest after the end of the water slide.

Figure 9 shows a person pushing a box from the bottom of a slope to the top of the slope.

Explain which one of the three distances shown in Figure 9 should be used to calculate the work done against the force of friction between the box and the slope.

Calculate the kinetic energy of a tennis ball travelling at 28 m/s. The mass of the tennis ball = 58 g.

Use the equation

kinetic energy =_........ J

Two cyclists ride on a hilly road and go through points P, Q, R and S.

The diagram in Figure 7 shows how the vertical height of the road changes during the journey from P to S.

The greatest overall change in gravitational potential energy for each cyclist is between which two points on the journey?

The total weight of one cyclist and bicycle is 700 N.

Calculate the total amount of work done against gravity when the cyclist travels from point P to point Q in the journey.

work done =_........ J

The gravitational potential energy of the other cyclist changes by 11 250 J when travelling from point Q to point R.

Calculate the mass of this cyclist.

Gravitational field strength = 10 N / kg

Use the equation

∆ GPE = m × g × ∆ h

mass =_........ kg

Explain why the total amount of work done by a cyclist between points Q and R is different from the change in gravitational potential energy of the cyclist between points Q and R.

The cyclists lubricated the chains and the wheel bearings of their bicycles before setting off.

Lubricating the chains and wheel bearings helps to

The kinetic energy of another cyclist is 2800 J.

The mass of the cyclist is 85 kg.

Calculate the velocity of this cyclist.

Use the equation

velocity =_........ m / s

A student lifts a toy car from a bench and places the toy car at the top of a slope as shown in Figure 9.

Describe an energy transfer that occurs when the student lifts the toy car from the bench and places the toy car at the top of the slope.

The student lets the toy car roll down the slope.

Describe how the student could find, by experiment, the speed of the toy car at the bottom of the slope.

The student needs to develop the experiment to determine the loss in potential energy and the gain in kinetic energy as the toy car is rolling down the slope.

State the other measurements the student must make.

When the toy car rolls down the slope, some energy is transferred to the surroundings as thermal energy.

State how the student could calculate the amount of energy transferred to the surroundings.

Explain one way the student could reduce the amount of thermal energy transferred to the surroundings as the toy car rolls down the slope.

A student lifts a toy car from a bench and places the toy car at the top of a slope as shown in Figure 1.

Describe an energy transfer that occurs when the student lifts the toy car from the bench and places the toy car at the top of the slope.

The student lets the toy car roll down the slope.

Describe how the student could find, by experiment, the speed of the toy car at the bottom of the slope.

The student needs to develop the experiment to determine the loss in potential energy and the gain in kinetic energy as the toy car is rolling down the slope.

State the other measurements the student must make.

When the toy car rolls down the slope, some energy is transferred to the surroundings as thermal energy.

State how the student could calculate the amount of energy transferred to the surroundings.

Figure 13 shows a drone.

The drone has four spinning blades.

The upward force produced enables the drone to rise in the air.

The speed at which the blades spin is measured in turns per minute.

Figure 14 shows how the upward force produced by the four blades depends on the speed at which the blades spin.

Describe the relationship between upward force and speed shown by this graph.

A different drone has a mass of 4.5 kg.

This drone rises from the ground to a height of 20 m.

Calculate the change in gravitational potential energy when the drone rises through a height of 20 m.

The gravitational field strength g = 10 N/kg.

change in gravitational potential energy =_........ J

State the amount of useful work done by the blades as the drone rises through 20 m.

useful work done =_........ J

It takes 4 s for the drone to rise through 20 m.

Calculate the useful power developed by the blades in this time of 4 s.

useful power developed =_........ W

*(c) The blades on the drone are turned by electric motors.

The electric motors are powered by a battery.

Figure 15 represents the energy transfers involved when the drone rises from the ground.

Describe the changes in the way energy is stored when the drone rises from the ground.

Your answer should refer to energy transfers.

Figure 4 shows a drone.

The drone has four spinning blades.

The upward force produced enables the drone to rise in the air.

The speed at which the blades spin is measured in turns per minute.

Figure 5 shows how the upward force produced by the four blades depends on the speed at which the blades spin.

Describe the relationship between upward force and speed shown by this graph.

A different drone has a mass of 4.5 kg.

This drone rises from the ground to a height of 20 m.

Calculate the change in gravitational potential energy when the drone rises through a height of 20 m.

The gravitational field strength g = 10 N/kg.

change in gravitational potential energy =_........ J

State the amount of useful work done by the blades as the drone rises through 20 m.

useful work done =_........ J

It takes 4 s for the drone to rise through 20 m.

Calculate the useful power developed by the blades in this time of 4 s.

useful power developed =_........ W

Figure 2 shows a way of projecting a small trolley up a sloping track.

When the button is pressed, a spring is released in P that projects the trolley up the track.

The trolley travels up the track, stops and then rolls back down.

The spring in P always exerts the same force when projecting the trolley.

A student investigates how the mass of the trolley affects the maximum vertical height, h, reached by the trolley.

State the measurements the student should make to complete the investigation.

You should make use of the equipment shown in Figure 2 and any other equipment that is needed.

Figure 3 is a graph of the student’s results.

The student states that the energy transferred by the spring is the same each time it is used.

Use data from any two points on the graph in Figure 3 to support this statement.

Describe how the student could extend the investigation to determine the average speed of the trolley as it rolls back down the track.

Which of these is the equation for work done?

A ball has a mass of 0.046 kg.

Calculate the change in gravitational potential energy when the ball is lifted through a vertical height of 2.05 m.

Use the equation

Δ GPE = m × g × Δ h

change in gravitational potential energy =_........ J

The ball is released.

Calculate the kinetic energy of the ball when the speed of the ball is 3.5 m/s.

kinetic energy of the ball =_........ J

The ball bounces several times.

Figure 7 shows how the height of the ball above the floor changes with time.

Use Figure 7 to estimate the maximum height that the ball reaches after the first bounce.

height after first bounce =_........ m

Explain why the ball does not bounce back to its starting height of 2.05 m.

A student plots a graph showing the height at the start and the maximum height reached after each bounce.

Figure 8 shows the student’s graph.

Describe how the maximum height reached changes with the bounce number in Figure 8.

Which of these is the equation for work done?

A ball has a mass of 0.046 kg.

Calculate the change in gravitational potential energy when the ball is lifted through a vertical height of 2.05 m.

Use the equation

Δ GPE = m × g × Δ h

change in gravitational potential energy =_........ J

The ball is released.

Calculate the kinetic energy of the ball when the speed of the ball is 3.5 m/s.

kinetic energy of the ball =_........ J

The ball bounces several times.

Figure 1 shows how the height of the ball above the floor changes with time.

Use Figure 1 to estimate the maximum height that the ball reaches after the first bounce.

height after first bounce =_........ m

Explain why the ball does not bounce back to its starting height of 2.05 m.

Figure 3 shows a spinning flywheel.

State how energy is stored in a spinning flywheel.

State one way to increase the amount of energy stored in the flywheel.

Figure 4 shows a skier going down a hill.

She descends through a vertical height of 200 m.

The skier’s mass is 65 kg.

Calculate the change in gravitational potential energy.

Use the equation

Δ GPE = m × g × Δ h

Take the gravitational field strength, g, as 10 N / kg.

change in gravitational potential energy =_........ J

At the bottom of the slope her speed was 36 m/s.

Calculate her kinetic energy at the bottom of the slope.

Use the equation

kinetic energy =_........ J

Describe how her speed at the bottom of the slope could be determined.

Which of these is a non-renewable source of energy?

Explain why renewable sources provide an increasing fraction of the electricity supply for many countries.

Electricity can be generated using a water turbine.

Water gains kinetic energy by falling from the top of a dam.

Calculate the minimum height that 7.0 kg of water must fall to gain 1300 J of kinetic energy.

minimum height =_........ m

As water enters the turbine at the bottom of the dam, the kinetic energy of 8.0 kg of moving water is 1100 J.

Calculate the speed of the moving water as it enters the turbine.

speed =_........ m/s

Moving air can be used to generate electricity using a wind turbine.

Figure 6 is a graph of kinetic energy against wind speed for a mass of moving air.

Just before the air reaches a wind turbine it has a wind speed of 15 m/s.

When the air has gone through the turbine it has a wind speed of 13 m/s.

As the air moves through the turbine some of its kinetic energy is transferred to the turbine.

Use the graph to determine the percentage of the kinetic energy transferred to the turbine from the air.

percentage of kinetic energy transferred from the air =_........ %

A cyclist is riding a bicycle at a steady velocity of 12 m/s.

The cyclist and bicycle have a total mass of 68 kg.

Calculate the kinetic energy of the cyclist and bicycle.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the cyclist uses the brakes to stop.

The cyclist starts to cycle again.

The cyclist does 1600 J of useful work to travel 28 m.

Calculate the average force the cyclist exerts.

average force =_........ N

*(d) A class of students investigate the power output of each student in the class.

The class must decide whether they use a method using steps or a method using weights. The whole class must use the same method.

Plan what measurements the students should take and how these can be used to calculate and compare the power output of each student.

You may draw a diagram to help with your plan.

A cyclist is riding a bicycle at a steady velocity of 12 m/s.

The cyclist and bicycle have a total mass of 68 kg.

Calculate the kinetic energy of the cyclist and bicycle.

Use the equation

kinetic energy =_........ J

Describe the energy transfers that happen when the cyclist uses the brakes to stop.

The cyclist starts to cycle again.

The cyclist does 1600 J of useful work to travel 28 m.

Calculate the average force the cyclist exerts.

average force =_........ N

An athlete uses a training machine in a gym.

The display on the machine shows the time spent on the machine and the amount of energy transferred during a training session.

Figure 3 shows the displays for two different sessions by the same athlete.

Explain what the displays show about the average power of the athlete in each of these two sessions.

Figure 5 shows the vertical forces on an aeroplane.

Use information from the diagram to determine the size and direction of the resultant vertical force on the aeroplane.

size =_........ kN, direction is_........

The aeroplane is descending.

Figure 6 shows a diagram of the resultant vertical and horizontal forces on the aeroplane as it is descending.

Complete the diagram to show the resultant of these two forces.

The mass of the aeroplane is 750 kg.

Calculate the change in gravitational potential energy of the aeroplane as it descends from 1300 m to the ground.

Gravitational field strength (g) = 10 N/kg

energy =_........ J

The aeroplane is powered by an engine that burns fuel.

The fuel supplies a total of 6500 kJ of energy every minute.

The efficiency of the engine is 0.70 (70%).

Calculate the power output of the engine.

Give your answer in kW.

power =_........ kW

Explain why the efficiency of the engine is less than 1 (100%).