Work , Power and Energy

- Work is said to be done when a force produces some displacement in a body.
- The amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force.

Work = Force x Displacement of point of application in the direction of force or W= Fx *S*

^{–}If there is no motion produced in the body even if a force acts on it, the work done is said to be zero,*e.*no work is done.- If a force
*F*is acting on a body and it displaces the body such that the displacement is at an angle*0*to the direction of force, then:

Work done = Force x Component of displacement

in the direction of force

or W= *F x S cos **θ*

- If the displacement. is in the direction of force,
*e.**θ**=*0°, then cos 0° = 1.

W= Fx *S*

In this case, the **work done is maximum and ****positive.**

- If the displacement is normal to the direction of
**force,***e.**θ**=*90°, then cos 90° = 0.

W= *F x S *cos 90″ = F *x 0= *0

Hence, the **work done **is zero.

- If the displacement is in a direction opposite to the force.
*e.**θ**= 180*°*cos*180°= —1.

W= *F *x *S *cos 180° = *–**FxS*

In this case, the work done is negative. This is usually the case when force opposes the motion or tries to stop a moving body.

- Work done by the force of gravity, W =
*mgh,*

where m = mass of the body, *g = *acceleration due to gravity, and *h = *height of the body from the earth’s surface.

The work done by the force of gravity is the same whether a person comes down from a certain height using a staircase or he comes down from the same height using a lift.

Since both force and displacement are vector quantities, therefore, **work **is a scalar quantity. In vector form, it is written as:

W= F.S

- The SI unit of work is joule abbreviated as J 1 joule of work is said to be done when a force o
**1**newton displaces a body through 1 metre,in it own direction. - The
**MKS unit**of work is**kg m**^{2 }s^{2} **The CGS unit**of work is**1**erg of work said to be done when a force of 1 dyne displaces

body through 1 cm in its own direction.