Topic: Work, Energy and Power

WEEK: 1 – 4

## Introduction

There is a link between work, energy, and power. You work when you walk, play, and dance. But you also need the power to do these things. Power is how fast you can do work. In this lesson, you’ll learn what work, energy, and power mean and how to figure out how much of each you have.

## Work

The amount of work done on an object is equal to the average force that is applied on the object and the distance it moves in the direction of the force. What this means is:

Work (W) = Force (F) X Distance (d)

The S.l. unit of work is Joule (J).

When you lift something, you do work because you use force to move it from one place to another (that is, distance). Remember that a Newton is the unit of force and a metre is the unit of distance.

Therefore, W = Fd

Joule = Newton X Metre J = Nm

Example 1

What is the work done in lifting a log of wood through a distance of 25 m, if 30 N of force is applied?

Solution

Force = 30 N Distances 25 m

30 N X 25 m

=    750 Nm

=    750 J

Example 2

A 50 kg bag of rice is lifted through a distance of 7 m. What is the work done in lifting the bag of rice? (Take g = 9.8 m/s2)

Solution

Mass (m) = 50 kg

Distance (d) = 7 m

Acceleration due to gravity (g) = 9.8 m/s’

Force (F)       =        Mass(m) X Acceleration (g)

F                     =        mg

=      50X9.8

=      490 N

Work done =               Force X Distance

W                    =        Fd

=      490 X 7

=      3430 J

Since 1 00OJ = 1 KJ

Therefore, W = 3.43 KJ

## Energy

Energy is the ability to do work. The SI unit of energy is the Joule (J). Chemical energy, mechanical energy, sound energy, heat energy, solar energy, and electrical energy are all different kinds of energy.

Mechanical energy comes in two forms: potential energy and kinetic energy. When an object is at rest, it stores energy as potential energy. Mathematically, it can be written as:

Potential energy (PE) = Mass (m) X Gravity (g) X Height (h) PE = mgh

Example 1

What is the potential energy possessed by a telephone of 2 kg resting on a table of height 7.2 m? (Take g = 9.8 m/s’)

Solution

Mass = 2 kg

Height = 7.2 m

Gravity = 9.8 m/s2

PE     =       mgh

PE     =  2 X 7.2 X 9.8

PE     =        141.12 J

Kinetic energy is the energy that an object has when it’s moving. It is based on how heavy the object is and how fast it is moving.

KE = J4 mv2

Example 2

Calculate the kinetic energy of a car of mass 300 kg moving at a velocity of 15 m/s’

Solution

KE      =     hmv2

m = 300 kg, v = 15 m/s2

KE      =     0.5 X 300 X 15

KE      =     2250J

## Power

Power is the rate of work done. The S.l. unit of power is Watt (W). It is mathematically calculated as:

Power = Work = Force X Distance

P = W = Fd = Fv

The S.l. unit of power. Watt (W) is the same as Joules per second. That is. W = J/s

Example

Determine the power of an engine of a car travelling at 25 m/s if it produces a force of ISO N. Solution

Power = Work = Force X Distance = Fv

F = ISO N, v = 25m/s

P = Fv

P = 150X25

P = 3 750 W