# How to solve questions on Work, Energy and Power

This article provides steps on how to solve questions on Work, Energy and Power. Therefore, the solutions below gives an easy step to how to solve questions on work, Energy, and Power for students writing Cambridge A level and other exams like UTME or Post UTME.

Power: It is the rate of energy expended per unit time. Its unit is Watt

Energy: It is the ability to do work .Its unit is Joule

**How to solve questions on Work, Energy and Power**

Question 1

A hammer with 10 J of kinetic energy hits a nail and pushes it 5.0 mm into a plank. Both the hammer and nail come to rest after the collision. What is the approximate average force that acts on the nail while it moves through 5.0 mm?{ Cambridge A level may/june 2016 p11}

A 0.050 N B 2.0 N C 50 N D 2000 N

Solution

workdone by a net force = change in kinetic energy of a body

F x s = Ek

F x s = 10

F x 0.005 = 10

F = 10 / 0.005

F = 2000N

D is the correct option

Q2, 3 and 4 are from cambridge A level may/june 2016 p13

Question 2

An object of mass 0.30 kg is thrown vertically upwards from the ground with an initial velocity of 8.0 m s–1. The object reaches a maximum height of 1.9 m. How much work is done against air resistance as the object rises to its maximum height?

A 4.0 J B 5.6 J C 9.6 J D 15 J

Solution

workdone by a net force = change in kinetic energy of a body

workdone = 1/2 m v2

v2 = u2 – 2as

v2 = 64 – 2*9.81*1.9

v2 = 64 – 37.278

v2 = 26.722

workdone = 1/2 * 0.3 * 26.722

workdone = 4.0 J

A is the correct option

Recommended: Short note on work, energy and power

Question 3

A racing car has an output power of 300 kW when travelling at a constant speed of 60 m s–1. What is the total resistive force acting on the car?

A 5 kN B 10 kN C 50 kN D 100 kN

solution

power = force x velocity

300000 = force x 60

force = 300000 / 60

force = 5000 = 5KN

A is the correct option

Question 4

The diagram shows the design of a water wheel which drives a generator to produce electrical power. The flow rate of the water is 200 kg s–1. The generator supplies a current of 32 A at a voltage of 230 V.

Ignoring any changes in kinetic energy of the water, what is the efficiency of the system?

A 14% B 16% C 22% D 47%

Solution

efficiency = power output / power input

power output = IV

power output = 32*230 = 7360

power input = flow rate * a * h

a is the acceleration due to gravity

power input = 200*8*9.81 = 15696

efficiency = (7360 / 15696)*100%

efficiency = 47%

Q 5 and 6 are from cambridge A level may/june 2016 p12

Question 5

A boy on a bicycle starts from rest and rolls down a hill inclined at 30° to the horizontal. The boy and bicycle have a combined mass of 25 kg. There is a frictional force of 30 N, which is independent of the velocity of the bicycle.

What is the kinetic energy of the boy and the bicycle after rolling 20 m down the slope?

A 1850 J B 2450 J C 3050 J D 3640 J

Solution

mgsinθ – fr = ma

25 * 9.81*sin30 – 30 = ma

122.625 – 30 = ma

92.625 = ma

ma is the net force

the kinetic energy = net force X distance

kinetic energy = 92.625 * 20 = 1852 J = 1850J

A is the correct answer

Question 6

An escalator in an underground station has 250 people standing on it and is moving with a velocity of 4.3 m s–1. The average mass of a person is 78 kg and the angle of the escalator to the horizontal is 40°.

What is the minimum power required to lift these people?

A 54 kW B 64 kW C 530 kW D 630 kW

Solution

the vertical force = mgsinθ = 250*78*9.81*sin40 = 122962 N

minimum power = vertical force x velocity = 122962 x 4.3 = 530 Kw

C is the correct option

Question 7

A man has a mass of 80 kg. He ties himself to one end of a rope which passes over a single fixed pulley. He pulls on the other end of the rope to lift himself up at an average speed of 50 cm s–1.

What is the average useful power at which he is working? (Cambridge A level May/June 2017 p13 q17)

A 40 W B 0.39 kW C 4.0 kW D 39 kW

Solution

Power is the rate of energy expended per unit time i.e power = energy/time = force x velocity

force = mass x acceleration due to gravity. note g in CIE is always 9.81ms-2

f = 80 x 9.81 = 784.8N

velocity in ms-1 = 50/100 = 0.5ms-1

power = 784.8 x 0.5 = 392.4 watt = 0.39KW (B is the correct answer)

Question 8

Calculate the apparent weight loss of a man weighing 70kg in an elevator moving downwards with an acceleration of 1.5ms-2.{2013 UTME Physics – Type U}

A. 105N B. 686N C. 595N D. 581N

solution

when an elevator is moving down

net force = ma

net force = 70*1.5

net force = 105 N

the weight loss = net force

the weight loss = 105 N

A is the correct option

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