Worksheet: Mechanical Power

In this worksheet, we will practice calculating the power required for a force to do an amount of work on an object in an amount of time.

Q1:

A train engine does work at a rate of 5,000 W. How much time will this engine take to do 125 J of work?

Q2:

A rocket moves vertically upward at a constant speed of 18 m/s. The weight of the rocket is 250 kN. What is the power supplied by the rocket’s engines? Give your answer in megawatts.

Q3:

A horse pulls a cart for 50 seconds. The work done by the force applied by the horse during this time is 37,500 J. What is the power supplied by the horse?

Q4:

360 W of power is supplied to do 270 J of work. How much time is taken to do this amount of work?

Q5:

A power of 140 W is supplied to do work for a time of 2.5 seconds. How much work is done?

Q6:

Which of the following formulas correctly shows the relationship between the time taken to do an amount of work and the power supplied to do the work?

  • A 𝑃 = π‘Š + 𝑑
  • B 𝑃 = π‘Š 𝑑
  • C 𝑃 = 𝑑 π‘Š
  • D 𝑃 = π‘Š βˆ’ 𝑑
  • E 𝑃 = π‘Š 𝑑

Q7:

A construction worker has to push a heavy, loaded waste container to a disposal area. This task tires the worker out and he pauses several times to rest. The distance that the container is moved in each 10-second time interval is shown in the table. Whenever the worker pushes the container, an average force of 80 N is used to push it. What is the average power supplied by the worker over the ten time intervals?

Time Interval Number 1 2 3 4 5 6 7 8 9 10
Distance (m) 2.3 1.1 0 1.6 0.7 0 0 1.2 1.1 0.5

Q8:

The power supplied by a force over a 10-second time interval is shown in the graph.

How much work does the force do from 𝑑 = 0 s to 𝑑 = 2 s?

How much work does the force do from 𝑑 = 3 s to 𝑑 = 5 s?

How much work does the force do from 𝑑 = 2 s to 𝑑 = 3 s?

How much work does the force do from 𝑑 = 5 s to 𝑑 = 9 s?

Q9:

The work done by a force over a 10-second time interval is shown in the graph.

What instantaneous power does the force supply at 𝑑 = 3 s?

What instantaneous power does the force supply at 𝑑 = 6 s?

What average power does the force supply between 𝑑 = 7 s and 𝑑 = 9 s?

Q10:

Suppose that 260 J of work is done in 40 seconds. What power is required to do this amount of work?

Q11:

How much work is done in 600 seconds by the force from a car engine that has a power of 1,250 W?

Q12:

The graphs (a), (b), (c), (d), and (e) show the change with time of forces acting on a car that travels at a constant speed while increasing the power from its engine. The force from the engine is shown in blue and the force that resists the car’s motion is shown in red. Which graph correctly shows the changes of the forces with time?

  • A(c)
  • B(e)
  • C(a)
  • D(b)
  • E(d)

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