Kinetic, elastic and gravitational potential energy

A person performs a ‘vertical box jump’.

Figure 4 shows five different stages, A, B, C, D and E, of the jump.

Complete the sentences.

Choose answers from the box.

The person in Figure 4 has a mass of 60 kg.

The person leaves the ground with a speed of 5.5 m/s.

Calculate the kinetic energy of the person.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

The person has a mass of 60 kg.

The height of the jump is 1.5 m.

gravitational field strength = 9.8 N/kg

Calculate the gravitational potential energy of the person at a height of 1.5 m.

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

The person jumps onto a box higher than the one in Figure 4, on page 12.

To jump onto a higher box, the person’s speed when leaving the ground is different.

Explain how the speed is different when jumping onto a higher box.

You should answer in terms of gravitational potential energy and kinetic energy.

Suggest one reason why a person is more likely to be injured when falling off a higher box.

A system is designed to store excess energy from the National Grid.

• Excess energy from the National Grid powers a motor that lifts a large cube.

• To transfer the energy back to the National Grid, the cube is allowed to fall.

• The falling cube turns a generator which produces electricity.

Figure 6 shows the cube before it is lifted and after it is lifted.

The cube has a density of 4200 kg/m³.

Determine the mass of the cube.

Use the Physics Equations Sheet.

Explain why the cube is made from a material with a high density.

The system is designed to store excess energy from the National Grid.

Explain how the efficiency of the system could be determined.

The system in Figure 6 on page 20 needs to be able to store excess energy as quickly as possible.

Explain one change to this system that would allow the same amount of energy to be stored more quickly.

Do not refer to efficiency in your answer.

Figure 2 shows an outdoor swimming pool.

The water in the swimming pool comes from the sea.

The water in the pool is heated using a geothermal energy resource.

Which of the following describes a geothermal energy resource?

Tick (✓) one box.

15 kg of seawater is heated before it is added to the pool.

specific heat capacity of seawater = 3800 J/kg °C

Calculate the change in thermal energy of 15 kg of seawater when its temperature is increased by 9.0 °C.

Use the equation:

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

The energy transferred from 1.0 m² of the surface of the pool to the air is 80 J each second.

The surface area of the pool is 120 m².

Calculate the energy transferred from the whole surface of the pool to the air each second.

Which of the following units is the same as 1 J/s?

Tick (✓) one box.

The pool is above sea level.

5.0 kg of water is pumped from sea level into the pool.

The water gains 196 J of gravitational potential energy.

gravitational field strength = 9.8 N/kg

Calculate the height of the pool above sea level.

Use the equation:

The water in some swimming pools is heated by burning fossil fuels.

Explain one environmental disadvantage of burning fossil fuels.

A drone is a miniature aircraft that has a remote control.

An inventor designed a battery powered drone.

The inventor tested what would happen if the battery runs out of charge during a flight.

Figure 5 shows the inventor about to launch the drone.

After the drone was launched, it moved at a constant speed and gained height.

The thermal stores of energy of the drone increased.

Describe two other changes to the energy stores of the drone as it moved at a constant speed and gained height.

When the drone reached a height of 840 m the motor was switched off.

The motor was switched back on after a short time, when the drone had fallen to a lower height above the ground.

The change in gravitational potential energy of the drone during the fall to this lower height was 3920 J.

The mass of the drone is 2.5 kg.

gravitational field strength = 9.8 N/kg

Calculate the height above the ground of the drone when the motor was switched back on.

Use the Physics Equations Sheet.

When the motor was switched off, the kinetic energy of the drone was 150 J.

Calculate the maximum possible speed of the drone when the motor was switched back on.

Use the Physics Equations Sheet.

Give your answer in km/s.

Figure 3 shows a person using a zip wire to move from a tree to the ground.

As the person moves down the zip wire, the block moves upwards.

What happens to the gravitational potential energy of the person as the person accelerates down the zip wire?

Tick (✓) one box.

What happens to the kinetic energy of the person as the person accelerates down the zip wire?

Tick (✓) one box.

The block is 3.4 m above the ground when the person is at the bottom of the zip wire.

mass of block = 2.5 kg

gravitational field strength = 9.8 N/kg

Calculate the gravitational potential energy of the block.

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

The trolley is a seat suspended from wheels which can roll along the zip wire.

When the person reaches the end of the zip wire, the person gets off the trolley.

The block falls downwards pulling the trolley back to the top of the zip wire.

maximum speed of block = 4.8 m/s

mass of block = 2.5 kg

Calculate the maximum kinetic energy of the block.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

As the trolley moves, work is done against friction.

What is the effect of this?

Tick (✓) one box.

The person oils the wheels on the trolley.

Explain how this will affect the speed of the person down the zip wire.

Figure 10 shows a child’s toy. A child pushes down on the toy to compress the spring. The spring then launches the toy into the air.

A student measured the maximum height reached by the toy. The student placed a vertical metre rule near the toy, and observed the height reached by the toy. The student repeated the experiment, observing from a different position. Figure 11 shows the toy at its maximum height and the two positions of the student.

Observing the toy from position B instead of position A affected the measurement of the maximum height reached by the toy. Explain how.

The greatest height reached by the toy was 64 cm. The gravitational potential energy of the toy at this height was 0.049 J. gravitational field strength = 9.8 N/kg Calculate the mass of the toy. Use the Physics Equations Sheet. Give your answer to 2 significant figures.

When the spring launches the toy into the air, the temperature of the air increases. Explain why the child’s toy on its own is not a closed system.

Figure 3 shows a lift near the bottom of a building.

The lift is attached by a cable to a counterweight.

An electric motor moves the lift.

The lift is moving up.

As the lift moves up, how far does the counterweight move down?

Tick (✓) one box.

What happens to the gravitational potential energy of the counterweight as it moves down?

Tick (✓) one box.

Calculate the change in gravitational potential energy of the lift when it moves up 4.0 m

The mass of the lift is 1300 kg

gravitational field strength = 9.8 N/kg

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

Complete the sentences.

Choose answers from the box.

Friction between the brakes and the cable causes the speed of the lift to decrease.

energy of the lift.

energy of the brakes.

The motor transfers different amounts of energy each time people use the lift.

Which factors affect the amount of energy transferred by the motor as the lift moves?

Tick (✓) two boxes.

The weight of the lift and the counterweight stretch the cable by 0.015 m

The cable acts like a spring with a spring constant of 880 000 N/m

Calculate the elastic potential energy of the stretched cable.

Use the equation:

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

A lift system using a counterweight is more efficient than a lift system that does not use a counterweight.

How does having a more efficient system affect the energy transferred by the motor?

Tick (✓) one box.

A trampoline is made from a sheet of material held in place by stretched springs. Figure 5 shows a child on a trampoline.

Position A shows the child’s maximum height above the trampoline. Position B shows the lowest position reached by the child when landing on the trampoline. Describe the changes to the stores of energy of the:

• child

• springs

• surroundings

as the child moves from position A to position B. Child

When the child is at position A, each trampoline spring is stretched by 0.056 m The elastic potential energy of each spring is 4.9 J When the child is at position B, the elastic potential energy of each spring increases to 8.1 J Calculate the extension of each spring when the child is at position B. Use the Physics Equations Sheet.

As the child bounces on the trampoline the child does work. What is the work done by the child equal to? Tick (✓) one box.

In a sport called far-leaping, an athlete uses a long pole to cross a river.

Figure 4 shows an athlete far-leaping.

Figure 5 shows the athlete in different stages of far-leaping.

Complete the sentence.

Choose answers from the box.

Between positions A and B the athlete speeds up. There is

a decrease in the athlete’s
store of energy.

Between positions B and C the athlete jumps to the pole and climbs up it.

Which statement describes a change in the athlete’s energy between positions B and C ?

Tick (✓) one box.

The pole falls over from position C. The athlete lets go of the pole and lands at position D.

The change in height of the athlete between positions C and D is 3.0 m.

mass of athlete = 50 kg

gravitational field strength = 9.8 N/kg

Calculate the change in gravitational potential energy of the athlete between positions C and D.

Use the equation:

change in gravitational = mass × gravitational field strength × change in height potential energy

The kinetic energy of the athlete at position D is 1600 J.

mass of athlete = 50 kg

Calculate the speed of the athlete at position D.

Use the equation:

Choose the unit from the box.

Figure 5 is repeated below.

At positions A and E, the athlete is standing still.

Why does the athlete have less energy in position E than in position A ?

Tick (✓) one box.

Athletes have a large power output when they are far-leaping.

What is meant by the power of an athlete?

Tick (✓) one box.

Figure 4 shows a sailing boat crossing an ocean.

There is a wind turbine on the boat.

The wind turbine generates electricity to charge a battery on the boat. Name one other renewable energy resource that could be used on the boat to generate electricity.

The boat also has a generator that burns a fossil fuel. The battery can be charged by either the wind turbine or the generator. Give two reasons why this is useful.

Explain one environmental impact of using fossil fuels to generate electricity.

The kinetic energy of the boat is 81 kJ. mass of boat = 8000 kg Calculate the speed of the boat.

As the boat passes over a wave, the gravitational potential energy of the boat increases by 19 600 J. mass of boat = 8000 kg gravitational field strength = 9.8 N/kg Calculate the change in height of the centre of mass of the boat as it passes over the wave.

Kangaroos are large animals that travel by jumping. Figure 8 shows a kangaroo.

Each leg of a kangaroo has a tendon connected to a muscle. Each tendon can be modelled as a spring. When a jumping kangaroo lands on the ground, the tendons stretch.

Figure 9 shows a sketch graph of how the maximum tendon length during a jump changes with the speed of the kangaroo.

Explain why a kangaroo can jump higher as its speed increases.

A kangaroo has a maximum gravitational potential energy during one jump of 770 J When the kangaroo lands on the ground 14% of the maximum gravitational potential energy is transferred to elastic potential energy in one tendon. The tendon has an unstretched length of 35.0 cm When the kangaroo lands on the ground the tendon stretches to a length of 42.0 cm

Calculate the spring constant of the tendon.

Figure 7 shows a toaster.

The toaster is connected to the mains supply using a three-core cable.

What is the function of the earth wire inside the cable?

Tick (✓) one box.

Complete the sentences.

Choose answers from the box.

The toaster is switched on for 120 seconds.

The power of the toaster is 850 watts.

Calculate the energy transferred by the toaster.

Use the equation:

energy transferred = power × time

Complete the sentences.

Choose answers from the box.

When bread is lowered into the toaster, a spring is stretched. The stretched spring

After the bread is toasted, the spring makes the toast move upwards. As the

the toast increases.

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

The toast was moved upwards by the spring.

The change in gravitational potential energy of the toast was 0.049 J

The mass of the toast was 0.050 kg

gravitational field strength = 9.8 N/kg

Calculate the change in height of the toast.

Figure 5 shows a girl skateboarding on a semi-circular ramp.

The girl has a mass of 50 kg

Calculate the gravitational potential energy (g.p.e.) of the girl at the top of the ramp.

Use the equation:

g.p.e. = mass × gravitational field strength × height

gravitational field strength = 9.8 N/kg

The girl has a speed of 7 m/s at the bottom of the ramp.

Calculate the kinetic energy of the girl at the bottom of the ramp.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

Not all of the g.p.e. has been transferred to kinetic energy.

Which two statements explain why?

Tick two boxes.

Explain how lubricating the wheels of the skateboard can increase the speed of the girl.

Use ideas about energy in your explanation.