8.1 Work, Power & Efficiency

A resultant force of 150 N acts on a ball and moves it up a slope, as shown in Figure 1.

Figure 1

What is the work done on the ball as a result of the movement?

The ball has a mass of 66 g.

[2]

Figure 2

Use Figure 2 to estimate the maximum height that the ball reaches after the first bounce.

[1]

A student plots a graph showing the height at the start and the maximum height reached after each bounce.

Figure 3 shows the student’s graph.

Describe how the maximum height reached changes with the bounce number in Figure 3.

Two cyclists ride on a hilly road and go through points W, X, Y and Z. The diagram in Figure 1 shows how the vertical height of the road changes during the journey from W to Z.

Figure 1

The greatest overall change in gravitational potential energy is between points

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ΔGPE = m × g × Δh

[2]

[2]

The two cyclists race each other from Y to Z, both starting from rest. The efficiency of each cyclist is shown in the table in Figure 2.

Figure 2

Determine which cyclist won the race using the information in the table in Figure 2.

Use the equation

The next time the cyclists went on this ride, they lubricated the chains and the wheel bearings of their bicycles before setting off.

Lubricating the chains and wheel bearings helps to

The work done to bring a car to rest is given by the equation

work done = braking force × braking distance

On the axes in Figure 1 below, sketch the variation of the car's braking distance with work done if a constant braking force is applied.

Figure 1

Before the car brakes, it has energy in its kinetic store.

This energy decreases as it brakes.

State what happens to the energy during braking.

Figure 2

The equation relating braking distance d to velocity v is

where C is a constant.

Use the equation and data from the graph in Figure 2 to calculate a value for C.

Give a unit for C.

Modern electric and hybrid cars are often fitted with a regenerative braking system.

A regenerative braking system not only slows a car down but a generator charges the car’s battery at the same time.

Discuss one of the benefits of a regenerative braking system. Explain how this benefit is possible.

A fairground amusement uses the arrangement shown in Figure 1 to measure the power rating of an individual.

Figure 1

In the table below, list the quantities that must be measured to determine power and an instrument that could be used for each measurement.

The mass of the load on the system is 30 kg.

The man pulled the rope as hard as he could for a total of 5.2 s. Detectors on the pulley determined that 2.3 m of rope passed through it.

The man inputs 2050 J of energy whilst pulling on the rope.

Calculate the percentage efficiency of the man's body.

Another fairground amusement involves a ball on a spring.

A student investigates how the energies of the ball and the spring change when they vibrate together.

The diagrams and bar charts in Figure 2 show how the energies of the ball and spring vary with the position of the ball.

The ball has a mass of 1 kg.

Figure 2

Use information from Figure 2 to describe the changes in energy, speed and position of the ball as it vibrates on the spring.

Figure 7

The drone has four spinning blades.

The upward force produced enables the drone to rise in the air.

The speed at which the blades spin is measured in turns per minute.

Figure 8 shows how the upward force produced by the four blades depends on the speed at which the blades spin.

Figure 8

Describe the relationship between upward force and speed shown by this graph.

A different drone has a mass of 4.5 kg.

This drone rises from the ground to a height of 20 m.

The gravitational field strength g = 10 N/kg.

[2]

change in gravitational potential energy = .............................................................. J

[1]

useful work done = .............................................................. J

[2]

useful power developed = .............................................................. W

This question is about energy changes.

Figure 11 shows a water slide.

A person travels from the top to the bottom of the water slide.

Figure 11

change in gravitational potential energy = m × g × h

[2]

change in gravitational potential energy = .............................................................. J

[2]

Figure 12

Explain which one of the three distances shown in Figure 12 should be used to
calculate the work done against the force of friction between the box and the slope.

(2)

(3)

kinetic energy = .............................................................. J

A cyclist is riding a bicycle at a steady velocity of 12 m/s.

The cyclist and bicycle have a total mass of 68 kg.

Calculate the kinetic energy of the cyclist and bicycle.

Use the equation

kinetic energy = ............................................... J

Describe the energy transfers that happen when the cyclist uses the brakes to stop.

The cyclist starts to cycle again.

The cyclist does 1600 J of useful work to travel 28 m.

Calculate the average force the cyclist exerts.

An athlete uses a training machine in a gym.

The display on the machine shows the time spent on the machine and the amount of energy transferred during a training session.

Figure 5 shows the displays for two different sessions by the same athlete.

Figure 5

Explain what the displays show about the average power of the athlete in each of these two sessions.

[1]

She descends through a vertical height of 200 m.

The skier’s mass is 65 kg. 

Take the gravitational field strength, g, as 10 N/ kg.

[2]

change in gravitational potential energy = .................................. J

Describe how her speed at the bottom of the slope could be determined.

Figure 9

Describe how the student could collect data to show how the rate of cooling of the container and water change with time.

Describe how the intensity of the radiation varies with wavelength in Figure 10.

Figure 11

[4]

gradient = .............................................................. unit ................................

[3]

Higher Only

Figure 14 shows the vertical forces on an aeroplane.

Figure 14

Use information from the diagram to determine the size and direction of the resultant vertical force on the aeroplane.

[2]

size = ................. kN, direction is ...............

Figure 15

Complete the diagram to show the resultant of these two forces.

[1]

[2]

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%).

[4]

power = ............................................... kW

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