CONCEPT OF WORK , ENERGY AND POWER .

CONCEPT OF WORK: 

In physics , work is said to be done whenever a force moves it point of application a distance in the direction of the force. Work is done whenever a force is applied in order to cause a body to move . For instance , if a boy push a car a certain distance or lift a load from one point to another or his stretched or compress an elastic body some distance , work is said to be done by the boy. 

   

Mathematically , W= F x S

Work done = force x perpendicular distance

 Where W = work done , F = force , S = distance covered by the body .

Work done is defined as the product of the force and the displacement in the direction of the applied force . It is measured in joules.

WORK DONE IN A FORCE FIELD:

What is force field ? 

There are two types of forces namely :

1. Contact forces  

2. Force fields .

Contact forces are forces which are encountered or in touch with the body to which they are applied . Examples are forces of push , pull , tension, frictional forces and reaction.

Force fields : these are forces whose sources do not require contact with the body to which they are applied . Examples are gravitational forces , electrostatic forces and magnetic forces .

Since gravitational field is an example of force field, in such field there is always a force pulling a body towards the center of the Earth. The weight of the body is the force of attraction on the body due to the Earth's gravity. The weight of the body acts downwards . In order to lift a load to a height , h , a pulling  Force must be applied to overcome the weight of the body . Therefore , when an object is lifted vertically upwards , work is done against the force of gravity or against the weight of the body .

Mathematically ; work done against gravity is given by ;

Work = force x distance 

Recall : F = mg 

Then ; work done =mg x h

        

W = mgh  ( where m = mass of the body, g = acceleration due to gravity and h = height ) N/B : g = 10 m/s² .

Suppose a boy of mass m , moves up a set of steps of total height, h , the work done by the boy  = his weight  x height .

         = mg x h 

         = mgh

Therefore, to lift a body against a force field, an opposing force is needed.

Hence , work done against gravity = 

weight of the body x the vertical upward displacement.

i.e work done against gravity by the boy

     =   mg x h 

W =   mgh 

In a force field, when a body falls freely , the Earth's gravitational field does work on the body . Suppose a body of mass m , falls through a vertical height, h , the work done by gravity on the body is given by : 

Work done = force x perpendicular height

Hence , W = mg x h .

Ex 1 : A boy of mass 20 kg runs up a set of steps of total height 5.0 m . Find the work done against gravity.

                    Solution:

Given; mass,m = 20 kg , height, h = 5 m , work done , W = ?

But g = 10 m/s² .

Using W = mgh

W = 20 x 10 x 5

W = 1000J.

Therefore, work done against gravity = 1000 Joules .

Ex 2: A loaded sack of total mass 200 kg falls down from the floor of a lorry 3 m high , find the work done by gravity on the load ?

                        Solution:

Given; mass , m = 200 kg , height, h = 3 m , 

g = 10 m/s²  , W = ? .

Using W = mg x h 

           W = 200 x 10 x 3

                 = 6000 J.

Therefore, the work done by gravity on the load= 6000 Joules .

Ex 3: A body is displaced through a certain distance x by a force of 30 N . If the work done is 100 J and the displacement is in the direction of the force, what is the value of x ?

                            Solution:

Given : force, F = 30 N , work done, 

W = 100 J , distance, S = x 

Work done = force x distance 

                     = F x S 

100 = 30 x X 

100 = 30x

Divide both sides by 30 

100/30 = 30x/30

10/3 = X 

X = 3.333 m .