Kinetic, elastic & gravitational potential energy

Figure 12 shows a student playing a game called ‘pool’.

In a game of pool, the player hits the white ball with a wooden cue.

Use the Physics Equations Sheet to answer questions 07.1 and 07.2.

Which equation links kinetic energy (E_k), mass (m) and speed (v)?

Tick () one box.

E_k = mv²

At one time during the game, the kinetic energy of the white ball is 0.0441 J.

The mass of the white ball is 0.180 kg.

Calculate the speed of the white ball.

The moving white ball collides with a stationary black ball.

Figure 13 shows the two balls before and after the collision.

Momentum is conserved in the collision.

What is meant by ‘momentum is conserved’?

Determine the velocity of the black ball after the collision. mass of white ball = 0.180 kg

mass of black ball = 0.160 kg

Use the Physics Equations Sheet.

Figure 1 shows two people wearing inflatable bodysuits.

The bodysuits are made of soft plastic and are inflated with air.

The inflatable bodysuits allow the two people to collide with each other safely.

The two people run towards each other before colliding and coming to a stop.

People wearing bodysuits take more time to stop during a collision than people not wearing bodysuits.

How does wearing bodysuits affect the deceleration of the people during the collision?

Tick (✓) one box.

The deceleration is less.

The deceleration is the same.

The deceleration is greater.

How does wearing bodysuits affect the impact force experienced by each person during the collision?

Tick (✓) one box.

The impact force is less.

The impact force is the same.

The impact force is greater.

Figure 2 shows person A about to collide with person B.

Person A has a mass of 60 kg.

Person A moves with a speed of 3.0 m/s.

Calculate the kinetic energy of person A.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

After the collision, person B has 45 J of kinetic energy.

Person B has a mass of 40 kg.

Calculate the speed of person B after the collision.

Use the equation:

Figure 3 shows a person in an inflatable sphere rolling down a hill.

Describe how the gravitational potential energy and kinetic energy of the person vary as the sphere rolls down the hill.

Suggest two factors that affect the maximum speed of the person as the sphere reaches the bottom of the hill.

Figure 7 shows two people wearing inflatable bodysuits.

The bodysuits are made of soft plastic and are inflated with air.

The bodysuits reduce the chance of injury in a collision.

Explain how wearing a bodysuit reduces the chance of injury in a collision.

Figure 8 shows person A about to collide with person B.

The arrows show the direction in which each person is moving.

The velocity of person A is + 2.0 m/s.

The two people collide and stop.

Calculate the velocity of person B before the collision.

Use the Physics Equations Sheet.

Figure 9 shows a person in an inflatable sphere rolling down a hill.

The total mass of the person and sphere is 80 kg.

The sphere moves through a vertical height of 6.4 m.

gravitational field strength = 9.8 N/kg

Calculate the maximum possible speed of the sphere at the bottom of the hill.

Use the Physics Equations Sheet.

The actual speed of the sphere at the bottom of the hill is much less than the maximum possible speed.

Explain why.

Figure 5 shows a person driving a bumper car at a theme park.

The mass of the bumper car and driver is 360 kg.

The bumper car moves with a speed of 1.50 m/s.

Calculate the kinetic energy of the bumper car and driver.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

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

Write down the equation which links efficiency, total power input and useful power output.

The motor of the bumper car has an efficiency of 0.80

The total power input to the motor is 220 W.

Calculate the useful power output of the motor.

The bumper car collides with a stationary barrier and stops.

What happens to the velocity of the bumper car during the collision?

A student investigated how the acceleration of a glider varied with the force causing the acceleration.

Figure 18 shows the equipment used.

The air blower allows the glider to move along the air-track with almost no friction.

This is the method used.

1. Line up the front of the glider with the marker.

2. Release the glider.

3. Record the velocity as the glider passes through the light gate.

4. Repeat steps 1 to 3 using different masses on the mass holder.

The student calculated the weight of each mass to determine the force causing the acceleration.

Which measurements does the datalogger need to calculate the velocity of the glider?

Tick (✓) one box.

The length of the card and the time taken to pass the light gate

The length of the string and the length of the card

The length of the string and the mass of the glider

The mass of the glider and the time taken to pass the light gate

Table 3 shows one set of results from the investigation.

Figure 19 shows the results.

What conclusion can the student make from the results in Figure 19 ?

Give a reason for your answer.

The 0.025 kg mass dropped through a height of 0.60 m.

Calculate the change in gravitational potential energy of this mass.

gravitational field strength = 9.8 N/kg

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

Another student used a wooden block pulled along a wooden board instead of a glider on an air-track.

Figure 20 shows the wooden block.

How would the friction between the wooden block and the wooden board compare with the friction between the glider and the air-track?

Tick (✓) one box.

The friction between the wooden block and the wooden board would be lower.

The friction between the wooden block and the wooden board would be the same.

The friction between the wooden block and the wooden board would be greater. 8

A student investigated how the acceleration of a glider varied with the mass of the glider.

The force causing the acceleration was constant.

Figure 13 shows the equipment used.

The air blower allows the glider to move along the air-track with very little friction.

This is the method used.

1. Line up the front of the glider with the marker.

2. Release the glider.

3. Record the velocity as the glider passes through the light gate.

4. Calculate the acceleration of the glider.

5. Repeat steps 1 to 4 using gliders of different mass.

The mass on the mass holder was 25 g.

The change in gravitational potential energy of the mass was 0.147 J.

gravitational field strength = 9.8 N/kg

Calculate the change in height of the mass.

Use the Physics Equations Sheet.

Figure 14 shows the results.

The student concluded:

‘The acceleration of the glider is inversely proportional to the mass of the glider.’

Explain why the student was correct.

Use data from Figure 14 in your answer.

A different student did the investigation using a trolley instead of an air blower and glider.

Figure 15 shows the equipment.

Give one way that the student could make the trolley roll more easily along the bench.

Figure 16 shows a student using a catapult to launch a small stone.

The catapult contains a spring.

What is the relationship between the extension of a spring and the force applied to the spring?

The extension of the spring is 20 cm.

The elastic potential energy stored by the spring is 1.16 J.

Calculate the spring constant of the spring.

Use the Physics Equations Sheet.

The student used the catapult to launch stone A and then stone B.

The spring had the same extension for each stone.

Stone B has a mass 4 times greater than stone A.

Explain the difference in the speed of stone A and the speed of stone B as they are launched from the catapult.

Your answer should include a calculation.

Use the Physics Equations Sheet.

Some catapults use a rubber band instead of a spring.

A student investigated how the extension of a rubber band varied with the force on the rubber band.

Figure 17 shows the results.

Explain why additional readings would allow the student to make a conclusion more easily.

Do not refer to repeat readings or calculating a mean.

Figure 1 shows a boat pulling a person parasailing.

A rope attaches the person to the boat.

What type of force is the weight?

Tick (✓) one box.

Contact force

Magnetic force

Non-contact force

The mass of the person is 75 kg.

Calculate the weight of the person.

gravitational field strength = 9.8 N/kg

Use the equation:

weight = mass × gravitational field strength

The resultant force acting on the person is zero.

Which of the following describes the motion of the person?

Tick (✓) one box.

Velocity decreasing

Moving at constant velocity

Velocity increasing

The horizontal force on the person is 4300 N.

Calculate the work done by this force in moving the person a horizontal distance of 500 m.

Use the equation:

work done = force × distance

Choose the unit from the box.

The speed of the boat changes.

The height of the person above the water decreases by 18 m.

Calculate the decrease in gravitational potential energy of the person.

mass of person = 75 kg

gravitational field strength = 9.8 N/kg

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

Ten-pin bowling is a game where a ball is rolled along the floor to knock over some wooden pins.

Figure 1 shows a person ten-pin bowling.

The speed of the ball was 8.0 m/s just after leaving the person’s hand.

The mass of the ball was 5.5 kg.

Calculate the kinetic energy of the ball.

Use the equation:

kinetic energy = 0.5 × mass × (speed)²

When the ball collides with the pins, energy is conserved.

What is meant by ‘conservation of energy’ when the ball collides with the pins?

Tick (✓) one box.

The gravitational potential energy of the pins is the same before and after the collision.

The kinetic energy of the ball is the same before and after the collision.

The total energy of the ball and pins is the same before and after the collision.

A machine returns the ball to the person.

The machine takes 25.0 s to return the ball to the person.

The useful power output of the machine is 660 W.

Calculate the work done by the machine in returning the ball to the person.

Use the equation:

work done = power × time

The machine has an efficiency of 0.60

The useful power output of the machine is 660 W.

Calculate the total power input to the machine.

Use the equation:

The machine has several moving parts.

What is the name of the force caused by the moving parts rubbing together?

What happens to the wasted energy from the machine?

Tick (✓) one box.

The wasted energy cools the surroundings.

The wasted energy heats the surroundings.

The wasted energy is destroyed.

Figure 12 shows the equipment a student used to investigate the effect of weight on the distance a box slides.

This is the method used.

1. Put a 1.0 N weight in the box.

2. Pull the box backwards until it reaches the start line, extending the rubber band by 10 cm.

3. Release the box.

4. When the box stops moving, measure the distance the box has slid using the metre rule.

5. Repeat steps 2 to 4 using a weight of 2.0 N and then 3.0 N.

The extension of the rubber band was a control variable in the investigation.

Suggest one other control variable in the investigation.

Table 4 shows the results when the weight inside the box was 1.0 N.

What was the uncertainty in the distance measurements when the weight inside the box was 1.0 N?

Tick (✓) one box.

±0.1 cm
±0.4 cm
±0.8 cm
±1.0 cm

The rubber band was extended by 10 cm.

The rubber band behaves like a spring with a spring constant of 36 N/m.

Calculate the elastic potential energy stored by the rubber band.

Use the Physics Equations Sheet.

What is the maximum possible value for the kinetic energy of the box?

Table 5 shows the student’s results.

Describe improvements the student could make to the method.

Use information from:

Figure 6 shows a wind turbine.

An alternating potential difference is produced when the wind turbine spins.

What is meant by ‘alternating potential difference’?

Figure 7 shows how the power output of a wind turbine varies with the length of the wind turbine blades when the wind speed is 20 m/s.

It is more economical to construct and use one wind turbine with 40-metre blades than two wind turbines with 20-metre blades.

Explain why.

Use information from Figure 7.

Predict the power output of a wind turbine with a blade length of 50 metres.

Tick (✓) one box.

10 000 kW

12 000 kW

14 000 kW

15 000 kW

The kinetic energy of the air passing the wind turbine blades each second is 73.9 MJ.

The mass of air passing the wind turbine blades each second is 236 000 kg.

Calculate the speed of the air passing the wind turbine.

Figure 9 shows a car travelling at a constant speed on a straight, level road.

Figure 10 shows a free body diagram for the car.

Explain how the free body diagram shows that the resultant force on the car is zero.

Table 4 shows how the braking distance of a car varies with the speed of the car.

A car decelerates from 24 m/s to 0 m/s

The work done by the brakes in decelerating the car is 210 000 J

Determine the mean braking force.

Use information from Table 4.

Give your answer to 2 significant figures.

The braking distance is directly proportional to the kinetic energy of the car.

Explain how the data in Table 4 supports this relationship.

A student investigated how the distance travelled by a trolley from the end of a ramp varied with the total mass of the trolley.

Figure 6 shows the equipment the student used.

This is the method used.

1. Put the trolley on the ramp at the start position.

2. Let the trolley roll down the ramp.

3. Measure the distance from the end of the ramp to the position where the trolley stops.

4. Repeat steps 1 to 3 with different masses on the trolley.

Give one variable the student should have kept the same in the investigation.

Table 4 shows the results.

Predict a value for X in Table 4.

What conclusion can be made from these results?

When the trolley was in the start position, the vertical height between the centre of mass of the trolley and the floor was 0.600 m

gravitational field strength = 9.8 N/kg

Calculate the gravitational potential energy of the trolley when the total mass of the trolley and masses was 2.50 kg

Use the equation:

gravitational potential energy = mass × gravitational field strength × height

When the trolley is released from the start position, energy is transferred in different ways.

Complete the sentences.

Choose answers from the box.

As the trolley moves down the ramp the trolley accelerates.

There is an increase in the trolley’s
energy.

After leaving the ramp the trolley slows down.

There is an increase in the
energy of

the surroundings.

Figure 10 shows a girl inside a train which is moving to the left at a speed of 20 m/s

The girl is wearing inline skates.

The train is moving at a constant speed of 20 m/s

The train suddenly decelerates.

The girl continues to move with a speed of 20 m/s

Which of Newton’s laws is a correct explanation of this situation?

Tick (✓) one box.

Figure 11 shows a velocity-time graph for the train as it arrives at a station and stops.

Between which two times on Figure 11 is the train stationary?

Tick (✓) one box.

The train travels at a constant speed between 0 seconds and 5 seconds.

Determine the distance the train travels between 0 seconds and 5 seconds.

Use the equation:

distance travelled = speed × time

Between which two times on Figure 11 is the deceleration of the train the greatest?

Write down the equation which links acceleration (a), change in velocity (Δ v) and time taken (t).

Determine the acceleration of the train between 15 seconds and 20 seconds.

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

At one point in the train’s journey the train’s speed was 6.0 m/s

At this point the kinetic energy of the train was 1 080 000 J

Calculate the mass of the train.