# Work

Work is the product of the force applied and the distance moved by the point of application of the force in the direction of the force.

Note that the distance moved has to be in the direction of the applied force. It is common that a force may be applied to move an object to the right, but instead the object moves to the left.

The force in this case has not done any work.

The S.I unit of work done is a joule (J)

Definition:
A joule is the work done when the point of application of a force of 1N, moves through a distance of 1m in the direction of the force.

Example: 1

1. Calculate the work done when a force of 9000N acts on a body and makes it move through a distance of 6m.

Solution
Force, F= 9000N
Distance, s = 6m

Work done = Force, F × Displacement, S

W= F×S

W= 9000×6

W= 54000J

Note:
If an object is raised vertically or falling freely, then the force causing work to be done is weight. Force = Weight = mass, m × acceleration due to gravity, g

Force = Weight= mg
Thus, the work done against gravity is given by;

Work done = Weight × height

Work done = mgh
Where m is mass in kg, h is distance in metres and some times, it is height.

Example:2
A block of mass 3kg held at a height of 5m above the ground is allowed to fall freely to the ground. Calculate the workdone.

Solution

Given, mass, m = 3Kg, Distance, s = 5m

Force F= Weight, W =mass × g

F= mg = 3×10

F = 30N

Work done = Force, F × Displacement, S

W= F×S

W= 30×5

W= 150J

Example: 3
A man of mass 80kg runs up a staircase of 10stairs, each of vertical height 25cm. Find the work done against gravity.
Solution:
Given, mass m = 80Kg,

Example: 4
A crane is used to to raise 20 tonnes of concrete to the top floor of a building 30m high. Calculate the total work done by the crane.
Solution:
Given, mass m = 20tonnes=20×1000=20,000Kg, Distance,h= 30m
Then;

Work done = Weight × height

Work done = mgh = 20,000×10×30
Work done = 6,000,000J

Example: 5
The figure bellow shows a bale of hay being pulled up an inclined plane with a force of 200N. The bale moves down the incline to a distance of 5m.

(i) Calculate the work done by the force.
Solution:

Work done = Force, F × Displacement, S

= 200N×(-5m)

Work done = -1000J