Kinetic, elastic and gravitational potential energy

Figure 10 shows a toy which is hung from a support.

When the handle is pulled down and then released, the toy bounces up and down.

When the handle is pulled down, the spring extends.

The extension of the spring is 0.35 m.

The spring constant of the spring is 5.6 N/m.

Calculate the elastic potential energy stored by the stretched spring.

Use the equation:

elastic potential energy = 0.5 × spring constant × (extension)²

Use the Physics Equations Sheet to answer questions 06.2 and 06.3.

Which equation links gravitational field strength (g), gravitational potential energy (E_p), height (h) and mass (m)?

Tick () one box.

When the handle is released, the toy moves upwards through a height of 0.60 m.

The toy has 0.294 J of gravitational potential energy in its highest position.

gravitational field strength = 9.8 N/kg

Calculate the mass of the toy.

Figure 11 shows the toy in three different positions.

The toy is released from position A and moves upwards.

The toy is moving upwards in position B.

The toy is at maximum height in position C.

Between position A and position B, the extension of the spring decreases.

How does the elastic potential energy stored by the spring change as the extension decreases?

Tick () one box.

Between position B and position C, the toy slows down.

How does the kinetic energy of the toy change as the toy slows down?

Tick () one box.

How does the gravitational potential energy of the toy change as the toy moves from position B to position C ?

Tick () one box.

The toy moves up and down many times before eventually stopping.

Which two of the following are reasons why the toy eventually stops?

Tick () two boxes.

Figure 11 shows a garden water feature.

The water feature has an electric motor that pumps water from the bottom container to the top container.

The pump transfers 0.343 J of gravitational potential energy to the water each second.

gravitational field strength = 9.8 N/kg

Determine the mass of water passing through the pump each second.

Use the Physics Equations Sheet.

The power of the pump motor is 4.86 W.

The resistance of the pump motor is 6.0 Ω.

Calculate the charge flow through the motor in 30 minutes.

Use the Physics Equations Sheet.

The pump motor breaks and is replaced with a new motor.

The new pump motor has the same power input, but has a greater efficiency.

Explain how the new pump motor would affect the flow of water in the water feature.

Figure 12 shows a device that accelerates a toy car at the start of a race track.

Pulling the handle compresses the spring in the device by 0.075 m.

When the handle is released, the energy stored in the compressed spring is transferred to the toy car.

spring constant = 64 N/m

mass of toy car = 0.052 kg

Calculate the maximum possible speed of the toy car just after the car starts to move.

Use the Physics Equations Sheet.

Give your answer to 2 significant figures.

Figure 13 shows the path of the toy car along a loop section of the race track.

The car moves along the track from position A to position B and then to position C.

Describe how the energy stores of the car change as the car moves along the track from position A to position C.

Ignore the effects of friction and air resistance.

At the end of the race track, the toy car passes through a light gate that measures the speed of the car.

Which two measurements are needed to determine the speed of the car?

Tick () two boxes.

In a ride at a theme park, a person is strapped into a pod that is attached to two stretched bungee cords.

The bungee cords behave like springs.

Figure 7 shows a person using the ride.

How is the extension of each bungee cord calculated?

Tick () one box.

Before the pod is released, the extension of each bungee cord is 7.5 m.

spring constant of the bungee cord = 800 N/m

Calculate the elastic potential energy stored in each stretched bungee cord.

Use the equation:

elastic potential energy = 0.5 × spring constant × (extension)²

The maximum speed of the pod is 15 m/s.

The mass of the pod is 240 kg.

Calculate the maximum kinetic energy of the pod.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

Use the Physics Equations Sheet to answer questions 03.4 and 03.5.

Which equation links gravitational field strength (g), gravitational potential energy (E_p height (h) and mass (m)?

Tick () one box.

The pod has 24 000 J of gravitational potential energy when at its maximum height.

The mass of the pod is 240 kg.

gravitational field strength = 9.8 N/kg

Calculate the maximum height reached by the pod.

Why is the maximum gravitational potential energy of the pod less than the initial elastic potential energy of the bungee cords?

Tick () two boxes.

Figure 1 shows a wind turbine.

Wind turbines may generate electricity when the electricity is not needed.

Two methods that can be used to store the energy from the turbine are:

Method A: Heating water to a high temperature.

Method B: Pumping water uphill into a reservoir.

Which energy store increases when water is heated?

Which energy store increases when water is pumped uphill into a reservoir?

Table 1 shows information about the two methods of storing energy.

Compare the advantages and disadvantages of the two methods of storing energy.

Include calculations in your answer.

Decreasing the amount of carbon dioxide released by different activities will help slow down climate change.

Transport and generating electricity are the two activities that released the largest amounts of carbon dioxide in the UK in 2018.

Explain one change that would reduce the amount of carbon dioxide released by each activity.

Generating electricity

In a ride at a theme park, a person is strapped into a pod that is attached to two stretched bungee cords.

The bungee cords behave like springs.

Figure 10 shows a person using the ride.

Which energy store increases as the bungee cords are stretched?

When the pod is released, the pod accelerates upwards.

Before the pod is released the extension of each of the two bungee cords is 8.0 m.

The spring constant of each bungee cord is 735 N/m.

The mass of the pod is 240 kg.

gravitational field strength = 9.8 N/kg

Calculate the maximum height reached by the pod.

Use the Physics Equations Sheet.

The actual maximum height reached by the pod will be lower than the correct answer to Question 06.2

Explain why.

The UK uses renewable energy resources to generate some of its electricity.

Figure 4 shows the proportion of electricity generated by different renewable energy resources in the UK in 2020.

Calculate the percentage of electricity generated using hydroelectric power.

A remote village in the UK uses a hydroelectric generator to provide electricity.

The mass of water that passes through the hydroelectric generator each day is 2 500 000 kg.

The change in vertical height of the water is 15.0 m.

gravitational field strength = 9.8 N/kg

Calculate the decrease in gravitational potential energy of the water.

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

Use the Physics Equations Sheet to answer questions 04.3 and 04.4.

Write down the equation which links energy (E), power (P) and time (t).

The hydroelectric generator transfers electrical power of 3000 W to the village.

Calculate the energy transferred to the village in 60 minutes.

The hydroelectric generator is turned by falling river water.

Figure 5 shows how the power output of the hydroelectric generator varied during one year.

Explain one reason why the power output varied.

Figure 8 shows a student before and during a bungee jump.

The diagram is not to scale.

In position B, the student is moving towards the river and the bungee cord is stretching.

How do the energy stores in position B compare with the energy stores in position A ?

Tick (✓) one box in each row.

The bungee cord behaves like a spring with a spring constant of 78.4 N/m.

At one point in the bungee jump, the extension of the bungee cord is 25 m.

Calculate the elastic potential energy stored by the bungee cord.

Use the equation:

elastic potential energy = 0.5 × spring constant × extension²

Table 5 shows information about different bungee cords.

Bungee cord C will have a smaller extension than A or B for any bungee jumper.

Give the reason why.

Which bungee cord would be safest to use for a person with a large weight?

Give a reason for your answer.

A baby bouncer is a harness attached to a spring that hangs from a door frame. Figure 7 shows a baby in a baby bouncer in two positions.

The baby bouncer should not be used with babies that have a mass greater than 12 kg. Suggest one reason why.

In positions A and B the baby is stationary. Describe the energy transfers as the baby moves from position A to position B.

In one position the extension of the spring is 8.0 cm. The elastic potential energy stored by the spring is 4.0 J. Calculate the spring constant of the spring. Use the Physics Equations Sheet.

Figure 1 shows a boy bouncing on a trampoline.

The boy falls from the position in Figure 1 towards the trampoline.

Complete the sentences.

Choose answers from the box.

As the boy lands on the trampoline, each spring stretches 0.015 m.

spring constant of each spring = 120 000 N/m

Calculate the energy stored by each spring.

Use the equation:

elastic potential energy = 0.5 spring constant (extension)²

There are 40 springs on the trampoline.

Calculate the total energy stored by the 40 springs when each spring is stretched by 0.015 m.

Use your answer from Question 01.2

The kinetic energy of the boy as he lands on the trampoline is 600 J.

The maximum kinetic energy of the boy after he bounces is 45% of his kinetic energy as he lands.

Calculate the maximum kinetic energy of the boy after he bounces.

Why is the kinetic energy of the boy after he bounces less than his kinetic energy as he lands?

Tick (✓) one box.

A girl ran to the top of some stairs.

Figure 2 shows the stairs.

The girl measured the height of the stairs.

What measuring instrument should she have used?

The height of the stairs was 1.7 m.

The mass of the girl was 50 kg.

gravitational field strength = 9.8 N/kg

Calculate the change in gravitational potential energy of the girl.

Use the equation:

gravitational potential energy = mass gravitational field strength height

A boy ran up the same stairs and did 1800 J of work.

The time it took the boy to run up the stairs was 1.44 s.

Calculate the power of the boy.

Use the equation:

Which stop-clock was used to measure the time the boy took to run up the stairs?

Tick (✓) one box.

Stop-clock A
Stop-clock B
Stop-clock C

The boy had a speed of 2.0 m/s at the top of the stairs.

The mass of the boy was 70 kg.

Calculate the kinetic energy of the boy at the top of the stairs.

Use the equation: kinetic energy = 0.5 mass (speed)²

Figure 11 shows a student launching a toy aeroplane. To launch the aeroplane, the student pulls on it to stretch the spring and then releases it.

Just before the toy aeroplane is released, the spring has an extension of 0.12 m. mass of aeroplane = 0.020 kg spring constant of the spring = 50 N/m Calculate the maximum speed of the toy aeroplane just after it is launched. Use the Physics Equations Sheet. Give the unit.

Complete the sentence. As the aeroplane moves upwards through the air there is a decrease in the energy of the aeroplane.

Give one factor which would increase the distance the toy aeroplane travels horizontally before hitting the ground.

Figure 11 shows a diver about to dive off a diving board.

Complete the sentences.

Choose answers from the box.

elastic potential gravitational potential kinetic nuclear

As the diver falls towards the water there is a decrease in

her energy.

As the diver falls towards the water there is an increase in

her energy.

Write down the equation which links kinetic energy (E_k), mass (m) and speed (v).

At the instant the diver hits the water, the kinetic energy of the diver is 5040 J.

The speed of the diver is 12 m/s.

Calculate the mass of the diver.

Most of the kinetic energy of the diver is transferred to the water.

How does this affect the thermal energy of the water?

Tick (✓) one box.

Figure 11 shows a toy car in different positions on a racing track.

The toy car and racing track can be modelled as a closed system. Why can the toy car and racing track be considered ‘a closed system’? Tick (✓) one box.

The car is released from rest at position A and accelerates due to gravity down the track to position B. mass of toy car = 0.040 kg vertical height between position A and position B = 90 cm gravitational field strength = 9.8 N/kg Calculate the maximum possible speed of the toy car when it reaches position B.

Figure 11 is repeated below.

At position C the car’s gravitational potential energy is 0.20 J greater than at position B. How much kinetic energy does the car need at position B to complete the loop of the track? Give a reason for your answer.

Tick () one box.

Figure 4 shows a theme park ride called AquaShute.

Riders of the AquaShute sit on a sled and move down a slide. There is a layer of water between the sled and the slide. How does the layer of water affect the friction between the sled and the slide? Tick (✓) one box.

The mass of one rider is 62.5 kg. The height of the slide is 16.0 m. gravitational field strength = 9.8 N/kg Calculate the gravitational potential energy of the rider at the top of the slide. Use the equation: gravitational potential energy = mass gravitational field strength height

At the bottom of the slide the speed of the rider is 12 m/s. The mass of the rider is 62.5 kg. Calculate the kinetic energy of the rider at the bottom of the slide. Use the equation: kinetic energy = 0.5 mass (speed)²

When a rider reaches the bottom of the slide, the sled decelerates and stops. Give two factors that will affect how far the sled will move before it stops.

Figure 9 shows a theme park ride called AquaShute. Riders of the AquaShute sit on a sled and move down a slide.

A light gate and data logger can be used to determine the speed of each rider and sled. What two measurements are needed to determine the speed of a rider and sled?

The decrease in gravitational potential energy of one rider on the slide was 8.33 kJ. The rider moved through a vertical height of 17.0 m. gravitational field strength = 9.8 N/kg Calculate the mass of the rider.

At the bottom of the slide, all riders and their sleds have approximately the same speed. Explain why.

Figure 4 shows a person sliding down a zip wire.

Describe how the vertical height of the tower could be measured accurately.

When using the zip wire, the person moved through a vertical height of 2.0 m The person has a mass of 45 kg gravitational field strength = 9.8 N/kg

Calculate the change in gravitational potential energy of the person. Use the equation: gravitational potential energy = mass × gravitational field strength × height

Give three factors that affected the kinetic energy of the person as she reached the bottom of the zip wire.

A scientist investigated how the maximum muscle power of humans varies with age and gender. The scientist asked volunteers to stand on a platform and to jump as high as they could. Figure 18 shows a volunteer taking part in the experiment.

An electronic timer measured the time that the volunteer was in the air.

The muscle power in watts per kg is calculated using the following equation:

One volunteer has a muscle power of 41 W/kg He was in the air for 0.12 s

Calculate his jump height.

Write down the equation which links kinetic energy, mass and speed.

One volunteer had a kinetic energy of 270 J and a speed of 3.0 m/s at the moment he left the ground. Calculate his mass.

Figure 19 shows the scientist’s results.

Compare the muscle power of males with the muscle power of females. Use data from Figure 19 in your answer.

The muscle power of each volunteer was measured five times. The highest muscle power reading was recorded instead of calculating an average. Suggest one reason why.

A scientist investigated how the maximum muscle power of humans varies with age and gender.

The scientist asked volunteers to stand on a platform and to jump as high as they could.

Figure 4 shows a volunteer taking part in the experiment.

An electronic timer measured the time that the volunteer was in the air.

The muscle power in watts per kg is calculated using the following equation:

One volunteer has a muscle power of 41 W/kg

He was in the air for 0.12 s

Calculate his jump height.

Write down the equation which links kinetic energy, mass and speed.

One volunteer had a kinetic energy of 270 J and a speed of 3.0 m/s at the moment he left the ground.

Calculate his mass.

Figure 5 shows the scientist’s results.

Compare the muscle power of males with the muscle power of females.

Use data from Figure 5 in your answer.

The muscle power of each volunteer was measured five times.

The highest muscle power reading was recorded instead of calculating an average.

Suggest one reason why.

Figure 9 shows a person sliding down a zip wire.

As the person slides down the zip wire, the change in the gravitational potential energy of the person is 1.47 kJ

The mass of the person is 60 kg

gravitational field strength = 9.8 N/kg

Calculate the change in vertical height of the person.

As the person moves down the zip wire her increase in kinetic energy is less than her decrease in gravitational potential energy.

Explain why.

Different people have different speeds at the end of the zip wire.

Explain why.

Figure 1 shows a cyclist riding along a flat road.

Complete the sentence.

Choose answers from the box.

chemical elastic potential gravitational potential kinetic

the cyclist increases.

The mass of the cyclist is 80 kg. The speed of the cyclist is 12 m/s.

Calculate the kinetic energy of the cyclist.

Use the equation: kinetic energy = 0.5 × mass × (speed)²

When the cyclist uses the brakes, the bicycle slows down.

This causes the temperature of the brake pads to increase by 50 °C. The mass of the brake pads is 0.040 kg. The specific heat capacity of the material of the brake pads is 480 J/kg °C.

Calculate the change in thermal energy of the brake pads.

Use the equation:

change in thermal energy = mass × specific heat capacity × temperature change

How is the internal energy of the particles in the brake pads affected by the increase in temperature?

Tick one box.

Figure 13 shows a lift inside a building.

Figure 13

The motor in the lift does 120 000 J of work in 8.0 seconds.

Calculate the power output of the motor in the lift.

Use the equation:

The power input to the motor is greater than the power output.

Tick two reasons why.

Figure 14 shows part of the circuit that operates the lift motor.

Figure 14

The lift can be operated using either of the two switches.

Explain why.

Write down the equation that links gravitational field strength, gravitational potential energy, height and mass.

The lift goes up 14 m. The total mass of the people in the lift is 280 kg.

gravitational field strength = 9.8 N/kg

Calculate the increase in gravitational potential energy of the people in the lift.

Give your answer to 2 significant figures.

Figure 16 shows a wind turbine.

Figure 16

At a particular wind speed, a volume of 2.3 ×10⁴ m³ of air passes the blades each second.

Calculate the mass of air passing the blades per second.

The power output of the turbine is directly proportional to the kinetic energy of the air passing the blades each second.

Describe the effect on the power output when the wind speed is halved.

At a different wind speed, the wind turbine has a power output of 388 kW.

The mass of air passing the wind turbine each second is 13 800 kg.

Calculate the speed of the air passing the blades each second.

Assume that the process is 100% efficient.