Question
When is the work done by a force said to be
(i) positive and (ii) negative?
Solution
(i) Positive work: when the force acting on the object is in the direction of displacement, then work done by a force is positive.
Positive work done is given by,
W = Fs cos 0° = Fs
Positive work done is given by,
W = Fs cos 0° = Fs
Examples:
(i) When a body falls freely under gravity (θ = 0°), the work done by the force of gravity is positive.
(i) When a body falls freely under gravity (θ = 0°), the work done by the force of gravity is positive.
(ii) When a horse pulls a cart, the applied force and displacement are in the same direction, the work done by the horse is positive.
(ii) Negative work: when the force acts in a direction opposite to the direction of displacement, work done is negative.
Negative work done is given by,
W = Fs cos 180°
= Fs (-1)
= - Fs
Examples:
(i) When a body is lifted up, the work done by the gravitational force is negative. Gravitational force is acting downwards and weight is lifted up.
Negative work done is given by,
W = Fs cos 180°
= Fs (-1)
= - Fs
Examples:
(i) When a body is lifted up, the work done by the gravitational force is negative. Gravitational force is acting downwards and weight is lifted up.
(ii) When brakes are applied to a moving vehicle, the work done by the braking force is negative. The braking force acts in the backward direction while the displacement of the vehicle is in the forward direction.
