Work is said to be done if a force displaces any object in any direction other than 90˚ to the direction of force applied.
If ‘F’ be the force applied and ‘d’ be the displacement and ‘θ’ be the angle between ‘F’ and ‘d’, work done by the force is,
W = Fcosθd
Work is a scalar quantity. Its SI unit is Joule.
a) When the angle between F and d is acute, the work done by the force is positive.
Eg:- Pushing a duster moves the duster in the direction of force. So θ=0˚ then,
W = Fdcosθ
= Fd [Work is positive]
b) When the angle between F and d is 90˚, the work done is zero.
Eg:- A coolie carry a load and walking on horizontal road does no work because the direction of force is vertical while he moves in horizontal direction. So,
W = Fdcos90˚
c) When the angle between F and d is 90˚<θ≤180˚, then work done is negative.
Eg:- When a body is pushed, it moves in the direction of force. Work done by the force is positive but the work done by friction is negative.
W = Frdcos180˚