Conservation & dissipation of 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 =_........

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 7 shows a ball being rotated in a horizontal circle.

Which arrow in Figure 7 shows the direction of the centripetal force on the ball?

The ball is moving at constant speed. Give one reason why the velocity of the ball is continuously changing.

Figure 8 shows a gymnast landing on a mat and coming to rest.

The gymnast has a mass of 53 kg.

The gymnast lands on the mat with a velocity of 4.0 m/s.

The average force exerted by the mat on the gymnast is 3500 N.

Calculate the time taken for the gymnast to come to rest.

Give your answer to an appropriate number of significant figures.

Use the equation

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

* (c) Figure 9 shows two trolleys, P and Q, moving at the same speed, v, directly towards each other.

The trolleys have the same mass.

When the trolleys collide, they stick together and stop.

Explain how momentum and energy are both conserved in this collision.

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.

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.

Figure 11 shows a pulley system that enables a person to lift a heavy barrel.

The person pulls down on the rope to make the barrel rise through 1.2 m.

The work done against gravity on the barrel is 1800 J.

Calculate the weight of the barrel.

Use the equation

work done = forcedistance moved in the direction of the force

weight of the barrel =_........ N

The efficiency of the system is 64%.

Calculate the total work done by the person.

Use the equation

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

Some energy is wasted due to friction.

Suggest another reason why some energy is wasted in using this pulley system.

*(b) A student has the equipment shown in Figure 12.

Devise an experiment to investigate how the efficiency of the pulley system varies with the weight of metal being lifted.

Your answer should include how you will use your measurements.

Which statement describes conservation of energy in a closed system?

A student uses the apparatus in Figure 9 to find out which of two materials, sand or sawdust, is the better insulator.

The student also has a kettle to boil water, a thermometer and a stop clock.

Draw a labelled diagram to show how the student should set up the equipment to investigate which material is the better insulator.

Give three factors that the student must control in this investigation.

Expanded polystyrene, used to insulate buildings, has different densities.

Figure 10 shows how the thermal conductivity of expanded polystyrene changes with the density of expanded polystyrene.

density of expanded polystyrene in kg/m³

Figure 10

Using the graph in Figure 10, describe how the thermal conductivity of expanded polystyrene changes with the density of expanded polystyrene.

Figure 11 is an energy diagram for an electric kettle, used to heat water.

one second = 2400 J

Calculate the amount of energy lost to the surroundings in one second.

energy lost to the surroundings in one second =_........ J

Calculate the efficiency of the kettle.

Use the equation

efficiency =_........

Which statement describes conservation of energy in a closed system?

A student uses the apparatus in Figure 1 to find out which of two materials, sand or sawdust, is the better insulator.

The student also has a kettle to boil water, a thermometer and a stop clock.

Draw a labelled diagram to show how the student should set up the equipment to investigate which material is the better insulator.

Give three factors that the student must control in this investigation.

Expanded polystyrene, used to insulate buildings, has different densities.

Figure 2 shows how the thermal conductivity of expanded polystyrene changes with the density of expanded polystyrene.

density of expanded polystyrene in kg/m³

Figure 2

Using the graph in Figure 2, describe how the thermal conductivity of expanded polystyrene changes with the density of expanded polystyrene.

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.

An electric water pump is powered by the 230 V mains supply.

Figure 5 shows the inside of the plug on the cable to the pump.

One wire in the plug is the earth wire.

The other two wires are

Describe the purpose of the component labelled X.

The 230 V mains supply transfers 9000 J of energy to the pump motor in 1 minute.

Calculate the current in the pump motor.

Use the equation

current =_........ A

The system transfers 8400 J of useful kinetic energy to the water passing through the pump in 1 minute.

Figure 6 shows a diagram of the energy transfers.

Explain why the useful energy transferred to the water is different from the total energy supplied to the pump.

Calculate the efficiency of the pump.

Use the equation

efficiency =_........

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.

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 7 shows an athlete using a fitness device.

The athlete stretches the spring in the device by pulling the handles apart.

The spring constant of the spring is 140 N/m.

The athlete does 45 J of work to extend the spring.

The athlete takes 0.6 s to expand the spring.

Calculate the useful power output of the athlete when stretching the spring.

useful power output of the athlete =_........ W

Calculate the extension of the spring.

Use an equation selected from the list of equations at the end of this paper.

extension of the spring =_........ m

A student investigates the stretching of a long piece of rubber.

Figure 8 shows the apparatus to be used.

Figure 8

The student puts just enough weight on the weight hanger to make the piece of rubber just tight.

The student wants to plot a graph to show how the extension of the piece of rubber varies with the force used to stretch it.

The student adds a known weight to the weight hanger.

Describe how the student could measure the extension of the rubber when he adds another weight to the weight hanger.

The student obtains a series of values of force and extension while loading the piece of rubber and then unloading it.

Figure 9 shows the graph of the student’s values.

Explain how the shape of this graph shows that the distortion of the piece of rubber being stretched is different from the distortion of a spring being stretched.

The area between the curve and the extension axis of a force/extension graph corresponds to work done or energy transferred.

Suggest what the shaded area of the graph in Figure 9 represents.

Which of these forces keeps the Moon moving around the Earth?

Which of these is a scalar quantity?

Figure 4 shows a box at rest on a floor.

The force that the floor exerts on the box is shown by the vector in Figure 4.

Figure 4

Add another vector to the diagram in Figure 4 to show the weight of the box.

Figure 5 shows part of a cart.

When the wheels turn the axles become warm.

Explain why the axles become warm when the wheels turn.

Give one way of reducing the heating of the axles when the wheels turn.

Complete the equation that relates efficiency, useful energy transferred by a device and total energy supplied to the device.

In one second an engine has a total energy input of 7500 J.

In one second 3200 J is transferred to the surroundings as wasted energy.

Calculate the useful energy transferred by the engine.

useful energy transferred =_........ J

Calculate the efficiency of this engine.

efficiency of the engine =_........

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%).