Kinetic, elastic and gravitational potential energy

Two students do an experiment to determine their power when running up a set of steps.

The diagram shows how they set up their experiment. Not all of the steps are shown in the diagram.

This is the students’ method.

• student A stands with a stopwatch at the top of the steps

• student A starts timing on the stopwatch and shouts “go” at the same time

• student B begins to run up the steps when she hears student A shout

• student A stops timing when student B reaches the top of the steps

The students repeat their method two more times.

Give a reason why the times recorded may not be accurate.

There are 24 steps in total and each step has a height of 19 cm.

Student B has a mass of 67 kg.

Show that student B gains about 3000 J of energy in her gravitational store when she runs up the set of steps.

The table shows the times recorded for student B.

Calculate the mean time from this data.

Give your answer to three significant figures.

Calculate the mean power of student B transferring energy to her gravitational store as she runs up the steps.

The students extend their investigation by calculating the power for students of different masses running up the steps.

The graph shows their results.

The students conclude that the greater the mass of the person, the greater the power of the person when running up the steps.

Comment on the students’ conclusion.

Fluorescent tube lamps can be used in schools and office buildings for lighting.

The photograph shows an engineer installing a fluorescent tube lamp.

Diagram 1 shows a simplified view of the components of a fluorescent tube lamp.

When the lamp is on, a large voltage is applied between the positive electrode and the negative electrode.

State what is meant by the term voltage.

The large voltage causes electrons to accelerate from the negative electrode towards the positive electrode.

An electron gains 1.0 × 10^–16J of energy when it accelerates between the electrodes.

Show that the voltage between the electrodes is about 600 V.

[magnitude of electron charge = 1.6 × 10^–19C]

The electron gains 1.0 × 10^–16J of energy in its kinetic store when it accelerates from the negative electrode to the positive electrode.

Calculate the speed of an electron when it reaches the positive electrode.

Assume the electron is initially at rest.

[electron mass = 9.1 × 10^–31kg]

When the electrons accelerate between the electrodes, they collide with mercury atoms.

Energy is transferred to the mercury atoms during the collisions. This causes the mercury atoms to emit ultraviolet light.

Atoms in the fluorescent coating absorb this ultraviolet light, which is then re‑emitted as light from a different part of the electromagnetic spectrum.

Diagram 2 shows this process.

Suggest why the tube must have a fluorescent coating for the lamp to operate effectively.

Explain why the fluorescent tube lamp is dangerous if the fluorescent coating becomes damaged.

A ball is moving through the air with a speed of 54.8 m / s. The ball has a mass of 159 g.

Calculate the energy in the kinetic store of the ball.

Give your answer to 3 significant figures.

The speed of the ball is measured using radio waves.

Radio waves of frequency 2.90 × 10¹⁰Hz travel towards the ball from a source.

The radio waves then reflect off the ball.

The reflected radio waves change frequency depending on the speed of the ball. This change in frequency is due to the Doppler effect.

The change in frequency can be calculated using this formula.

Show that the change in frequency of the radio waves is approximately 1.1 × 10⁴Hz.

[speed of radio waves = 3.00 × 10⁸m / s]

The change in frequency of the radio waves happens because the ball acts as a new source of radio waves.

The ball is moving away from the original source of radio waves.

Explain the change in frequency of the radio waves when the radio waves reflect off the ball.

The photograph shows the tidal power station across the estuary of the river Rance in France.

The diagram shows a simplified view of the tidal power station.

At high tide, water is trapped behind the tidal barrier.

At low tide, the trapped water is released through the turbine shaft. This causes a turbine to spin, which generates electricity.

Give two advantages of generating electricity using tidal power.

Give two disadvantages of generating electricity using tidal power.

At low tide, water flows through the turbine shaft.

As the height of the trapped water in the river decreases, water falls through a height of 8.0 m to reach the turbine shaft.

Calculate the energy transferred from the gravitational store of the water when 1.0 kg of water flows through the turbine shaft.

Use the formula

change in gravitational potential energy = mass × g × height

The tidal power station has a maximum power output of 240 000 kW when water falls through a height of 8.0 m.

Calculate the mass of water flowing through the turbine shaft in 1 second when the power station is operating at maximum power.

Assume the power station is 100% efficient.

An athlete jumps vertically from the ground.

The athlete has a mass of 85 kg, and leaves the ground with an upwards velocity of 4.5 m/s.

State the formula linking kinetic energy, mass and speed.

Calculate the athlete’s kinetic energy at a speed of 4.5 m/s.

At the maximum height of the jump, the athlete has a speed of 0 m/s.

State the increase in the amount of energy in the athlete’s gravitational potential energy store from the ground to the maximum height of the jump.

State the formula linking gravitational potential energy, mass, gravitational field strength and height.

Calculate the maximum height of the athlete’s jump.

Sketch a velocity‑time graph for the athlete’s jump from the ground to the maximum height of the jump. No numbers are required.

Assume there is no air resistance.

What feature of the velocity‑time graph gives the acceleration due to gravity?

Explain why the gravitational field strength on the Moon is different from the gravitational field strength on the Earth.

The photograph shows a wind turbine used for supplying energy on a large scale.

Describe a change in the turbine’s energy stores from when the turbine is at rest to when it is moving at full speed.

Describe a change in the turbine’s energy stores when the wind is blowing but the turbine moves at constant speed.

State the formula linking efficiency to useful energy output and total energy output.

The wind transfers 1.2 × 10⁶J of energy to the turbine.

The total mass of the turbine blades is 16 000 kg.

The wind causes the turbine blades to accelerate from rest to an average speed of 7.6 m/s.

Calculate the efficiency of the turbine.

The diagram shows the collision between two balls, A and B.

The masses and velocities of both balls are shown before and after the collision.

Ball B is stationary before the collision.

0.265 kg
0.265 kg

Before collision
After collision

When the balls collide, ball B applies a force on ball A, which causes the velocity of ball A to change.

Ball A also applies a force on ball B during the collision.

Describe how the force applied on ball A compares with the force applied on ball B during the collision.

Calculate the momentum of ball A before the collision.

momentum of ball A before collision =_........ kg m / s

Show that the velocity, v, of ball B after the collision is about 0.6 m / s.

A collision is considered elastic if the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Using data from the diagram, deduce whether this collision is elastic.

The photograph shows a toy called a marble run.

A student lifts a marble from the table to the top of the marble run at point A. They release the marble from point A and it rolls through pipes to reach the bottom of the marble run at point B.

The marble leaves the marble run at point B and rolls across the table.

As the marble rolls, energy is transferred due to the different forces acting on the marble.

Describe the energy transfers from before the student lifts the marble to when the marble reaches point B of the marble run.

The student wants to measure how much energy the marble loses as it moves from point A to point B.

The student needs to measure the speed of the marble as it leaves the marble run at point B.

Describe a method the student could use to measure this speed.

The difference in height between point A and point B is 0.21 m.

The mass of the marble is 5.5 g.

The marble leaves the marble run at point B with a speed of 0.76 m/s.

Calculate the energy lost by the marble as it rolls from point A to point B.

A model electric motor is used to lift a load through a vertical height.

The load has a mass of 400 g and gains 3.2 J of energy in its gravitational store when lifted.

State the formula linking gravitational potential energy, mass, gravitational field strength (g) and height.

Calculate the height the load is lifted.

State the amount of useful work done on the load by the motor when the load is lifted through this height.

The load is lifted at a constant speed.

Diagram 1 shows the lifting force acting on the load as it is lifted.

Draw a labelled arrow on diagram 1 to show the other force acting on the load.

Ignore the effects of air resistance.

Diagram 1

A joulemeter measures the amount of energy transferred electrically to the motor as the motor lifts the load.

The joulemeter displays a reading of 11.0 J when the load has gained 3.2 J of energy in its gravitational store.

Calculate the efficiency of the motor.

Justify why 7.8 J of energy must be dissipated into the thermal store of the surroundings as the load is lifted.

Diagram 2 is an incomplete Sankey diagram.

Complete the Sankey diagram to show the energy transferred by the motor.

The diagram shows the inside of an oscilloscope.

Electrons leave the electron supply and accelerate towards the screen.

The stream of electrons hits the screen.

The grid is connected to the positive terminal of a high voltage power supply.

Explain, in terms of the movement of particles, how the grid has become positively charged.

State the formula linking kinetic energy, mass and speed.

Calculate the speed of an electron when it has 1.3 × 10^–15J of kinetic energy.

The mass of an electron is 9.1 × 10^–31kg.

The stream of electrons spreads out as it travels towards the screen.

Explain why the electrons in the stream move apart from each other.

The oscilloscope can cause the electrons to move in a circle.

This produces a circular pattern on the screen.

Use the scale to determine the radius of the circle.

The time taken for the electrons to complete one orbit of the circle is 24 ms.

Calculate the orbital speed of the electrons.

Use the formula

A teacher demonstrates the penetrating ability of alpha, beta and gamma radiation from some radioactive sources.

State a precaution the teacher should take to make sure they are working safely with the radioactive sources.

State the name of a detector the teacher could use to detect the radiation from each source.

Draw crosses () in the table to show which type of radiation cannot penetrate each material in the table.

An alpha particle of mass 6.610^–27kg travelling at a speed of 2.110⁷m/s hits a sheet of paper.

Calculate the kinetic energy (KE) of the alpha particle.

State the work done on the alpha particle when its speed is reduced to 0 m/s by the sheet of paper.

State which energy store of the paper increases when the alpha particle is stopped.

Diagram 1 represents the atoms of a gas inside a container.

Diagram 1

Explain how the atoms exert a pressure on the walls of the container.

Explain why the pressure of the gas in the container decreases as its temperature decreases.

The volume of the container does not change.

Diagram 2 shows a device called a magneto-optical trap (MOT).

Physicists use the device to cool gases to extremely low temperatures.

The MOT uses laser beams and magnetic fields to trap a small collection of atoms with extremely small kinetic energies.

Each trapped atom has a mass of 5.0 × 10^–27kg and a mean speed of 73 m / s.

Calculate the temperature of the trapped atoms.

[mean kinetic energy of an atom = 2.1 × 10^–23 × temperature in kelvin]

The photograph shows a vertical drop ride at an amusement park.

The car is pulled to the top of a vertical shaft and then released from rest.

The car then falls freely because of the force of gravity.

Calculate the speed of the car when it has fallen 18 m.

State the formula linking kinetic energy, mass and speed.

The mass of the car and its passengers is 2.1 tonnes.

Calculate the kinetic energy of the car when it has fallen 18 m.

[1 tonne = 1000 kg]

The actual speed of the car when it has fallen 18 m is lower than the value calculated in (a).

Describe the energy transfers occurring from immediately before the car was released to when the car has fallen 18 m.

Refer to stores and transfers in your answer.

This question is about a parachutist.

A parachutist leaves a helicopter that is hovering above the ground.

The parachutist is initially at rest and falls vertically downwards.

Calculate the speed of the parachutist after they have fallen through a distance of 1300 m.

Ignore the effect of air resistance.

When the parachutist is much nearer to the ground, they open their parachute.

The parachutist slows down.

Explain the change in speed of the parachutist.

Use ideas about forces in your answer.

It is observed that from when the parachute opens to just before the parachutist touches the ground, the GPE store and the KE store of the parachutist both decrease, yet energy is still conserved.

Justify these observations.

The diagram shows a ball at the bottom of a ramp. The ball moves up the ramp with an initial speed v.

State the formula linking gravitational potential energy (GPE), mass, gravitational field strength (g) and height.

The ball has a mass of 14 g.

Show that when the ball reaches a height of 29 cm above the bottom of the ramp, the GPE gained by the ball is about 4 10⁻²J.

At the bottom of the ramp, the 14 g ball has a kinetic energy (KE) of 5.1 10⁻²J.

Calculate the speed of the ball at the bottom of the ramp.

The ball is stationary when it reaches the top of the ramp. There is a difference between the KE of the ball at the bottom of the ramp and the GPE of the ball at a height of 29 cm above the bottom of the ramp.

Explain why the work done by friction between the ball and the ramp is equal to this difference.

A student uses a computer simulation to investigate the motion of particles in a gas.

He records the pressure of the gas and the mean speed of the particles in the gas at different temperatures.

The graphs show his results.

Give a reason why the student does not start the y-axis scale from zero on either of his graphs.

Describe the relationships shown by the graphs.

Explain why the value of temperature chosen in the simulation should not decrease below – 273 °C.

The student then calculates the kinetic energy of a single gas particle at each temperature.

Using the curve of best fit on graph 2, determine the mean speed of a gas particle when the gas temperature is 100 °C.

The mass of a single gas particle is 5.3 × 10^–26 kg.

Calculate the average kinetic energy of a gas particle when the temperature of the gas is 100 °C.

Calculate the temperature of the gas in kelvin when its temperature is 100 °C.

On the axes, sketch a graph of the average kinetic energy of the gas particles against temperature in kelvin.

A student uses this apparatus to investigate the force needed to pull a block along a ramp.

State the formula linking work done, force and distance moved in the direction of the force.

The student pulls the block 0.89 m along the ramp with a force of 26 N.

Show that the work done on the block by the 26 N force is about 23 J.

The block has a mass of 1.3 kg and moves vertically upwards 0.11 m.

Calculate the increase in the gravitational potential energy (GPE) store of the block between the bottom and the top of the ramp.

Explain why the work done to move the block along the ramp is greater than the increase in the GPE store of the block.

The student suggests it is better to use a less steep ramp to raise the block through the same vertical height.

Discuss an advantage and a disadvantage of using a less steep ramp.

The diagram shows part of a device used to demonstrate electrostatic charge.

Negatively charged water droplets fall into bucket A.

Describe how bucket A becomes negatively charged.

Explain why the negatively charged droplets spread out as they fall.

A droplet hits bucket A with a speed of 3.8 m/s.

Calculate the kinetic energy of the droplet when it hits bucket A.

The total charge stored in bucket A is –1.110^–10 C.

This charge passes through the air between the buckets in 9.2 × 10^–3 s, causing a spark between bucket A and bucket B.

Calculate the mean current between the buckets.

The spark transfers a charge of –1.110^–10 C.

The mean voltage between the buckets is 1.7 kV.

Calculate the energy transferred by the spark.

When a meteor explodes, light waves and sound waves are produced at the same time.

State the formula linking average speed, distance moved and time taken.

A person standing 1860 m away from the site of a meteor explosion hears the sound of the explosion 5.6 s later.

Calculate the speed of sound in air.

A scientist stands a long way from the meteor explosion.

Explain why he hears the explosion at a different time to when he sees it.

Sound is a longitudinal wave.

Describe what is meant by the term longitudinal wave.

In 2013, a meteor exploded above Russia.

Just before the meteor exploded, it was travelling at a speed of 19.2 km/s.

The mass of the meteor was estimated to be 1.25 × 10⁷kg.

State the formula linking kinetic energy, mass and speed.

Calculate the energy in the kinetic store of the meteor just before the meteor exploded.

A student uses this apparatus to investigate how the efficiency of an electric motor varies with its input voltage.

This is the student’s method.

• connect the electric motor to a d.c. power supply and a joulemeter

• attach a 1.0 kg mass to the electric motor using a length of string

• set the voltage of the power supply to 10 V and switch on the power supply

• switch off the power supply when the mass has been lifted through a distance of 50 cm

• record the input energy to the motor from the joulemeter

• calculate the energy transferred to the gravitational store of the mass

• calculate the efficiency of the motor

The student repeats this process, setting the power supply to a different voltage each time.

State how the student could improve the reliability of her results.

Give two control variables for the investigation.

Show that the gravitational store of the 1.0 kg mass increases by 5.0 J when it is lifted through a distance of 50 cm.

The table shows the student’s results.

Calculate the motor efficiency when the power supply is set to a voltage of 10 V.

Plot a graph of the motor efficiency on the y-axis against the power supply voltage on the x-axis.

Draw a curve of best fit.

Using the graph, determine the minimum power supply voltage that will allow the electric motor to operate at maximum efficiency.

A metalworker uses a hammer of mass 1.8 kg to deform a piece of metal on an anvil.

Calculate the increase in the hammer’s gravitational potential energy (GPE) store when the hammer is raised through a height of 0.95 m above the metal.

[GPE gained = mass × gravitational field strength × height]

The metalworker moves the hammer down to strike the metal.

The hammer must have at least 21 J of energy in its kinetic energy (KE) store as it hits the metal to deform it.

Explain why the metalworker must do at least 4 J of mechanical work on the hammer to deform the metal.

Calculate the velocity of the hammer just before it strikes the metal.

[KE of hammer = 21 J]

When the hammer hits the metal, the hammer comes to rest without rebounding.

Calculate the mean (average) force needed to bring the hammer to rest in a time of 0.12 s.