Questions of efficiency

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P1a: 10

Efficiency

Questions of efficiency

The efficiency of a machine can be worked out using the equation:

Efficiency = useful energy output total energy input

Use this equation to answer the following questions:

1

An engine has an energy input of 100 J and gives out 27 J of useful kinetic energy. What is the efficiency of the engine?

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2

A hair dryer has an energy input of 1500 J and gives out 1300 J of useful energy. What is the efficiency of the hair dryer?

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3

Compare these two machines to decide which is more efficient.

i

Machine A uses 1000 J of energy to do 300 J of useful work.

ii

Machine B uses 500 J of energy to do 200 J of useful work.

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4

Compare these two cranes to decide which is the more efficient.

i

Crane A uses 800 J of energy to do 350 J of useful work.

ii

Crane B uses 750 J of energy to do 300 J of useful work.

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P1a: 10

continued

5

Look at these energy diagrams. Work out the efficiency of each device.

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6

The motor for a lift in a tall building uses 12 000 W of power. The lift and its passengers has a mass of 500 kg. The lift motor takes 10 s to raise the lift and its passengers through a height of

20 m. Work out the efficiency of the lift motor.

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P1a: 10

Answers to Worksheets

Worksheet P1a: 10

1

27 ÷ 100 = 27%.

2

1300 ÷ 1500 = 87%.

3

Machine A efficiency: 300 ÷ 1000 = 30%. Machine B efficiency: 200 ÷ 500 = 40%.

4

Crane A efficiency: 350 ÷ 800 = 44%. Crane B efficiency: 300 ÷ 750 = 40%.

5

Hydrogen fuel cell efficiency: 650 ÷ 1000 = 65%. Steam-diesel hybrid efficiency:

200 ÷ 500 = 40%. Electric car efficiency: 480 ÷ 600 = 80%.

6

Total work done by lift = mass

10

height = 500

10

20 = 100 000 J. Work done each second = 100 000 ÷ 10 = 10 000 J. Efficiency = 10 000 ÷ 12 000 = 83%.

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