# Work

What is Work ?

A force must be applied for work to be completed, and there must also be motion or displacement in the force’s direction. The amount of force multiplied by the distance moved in the force’s direction is known as the work done by a force acting on an object. Work has no direction and only magnitude. Work is a scalar quantity as a result.

Formula of Work

The product of a force’s component acting in the displacement’s direction and its magnitude is known as the work that a force performs.

W stands for the amount of work completed, F is the applied force, s stands for the displacement, denotes the angle formed by the force and displacement, and F Cos θ is the force’s component in the direction of displacement.

No work is done if there is no displacement, regardless of how much force is applied, according to the work equation. In conclusion, we can state that no work is completed if

There is no displacement.
There is no force.
The relationship between the force and displacement is perpendicular.

### Unit of Work

The SI unit of work is Joule (J).

1 J = 1 N ⋅ m = 1 kg ⋅ m2/s2.

The C G S unit of work is erg.

1 Erg = 1 dyn.cm = 1 g cm2 /s2

example, if a force of 5 newtons is applied to an object and moves 2 meters, the work done will be 10 newton-meter or 10 Joule.

Example of Work
Q. An object is horizontally dragged across the surface by a 200 N force acting parallel to the surface. Find out the amount of work done by the force in moving the object through a distance of 18 m.

Solution:

Given:

Force (F) = 200 N, Distance (d) = 18 m

Since F and d are in the same direction, θ = 00, [θ is the angle of the force to the direction of movement], therefore

W = F d Cos θ

W = 200 x 18 x Cos 00

W = 3600 J [Since Cos 00 = 1]