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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.

capture

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 6are 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

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
short note on work, energy and power

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