What is Work?
Work is said to be done whenever a force acts on a body and the body moves through some distance in the direction of the force. Thus, work is done on a body only if the following two conditions are satisfied:
(i) A force acts on the body.
(ii) The point of application of the force moves in the direction of the force.
Examples:
Work is done when a horse pulls a cart, an engine pulls a train, a man goes up a hill, etc.
Nature of Work Done in Different Situations
Positive work:
If a force acting on a body has a component in the direction of the displacement, then the work done by the force is positive.
when θ is acute, cos θ is positive. ∴ W = Fs cos θ = a positive value
Examples:
(i) When a body falls freely under gravity (θ = 0°), the work done by the 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.
(iii) When a gas filled in a cylinder fitted with a movable piston is allowed to expand, the work done by the gas is positive, because the force due to gas pressure and displacement act in the same direction.
(iv) When a spring is stretched, both the stretching force and the displacement act in the same direction. So, work done is positive.
Negative work:
If a force acting on the body has a component in the opposite direction of displacement, the work done is negative. As shown in Fig. 6.4, when θ is obtuse, cos θ is negative.
∴ W = Fs cos θ = a negative value
Examples:
(i) When a body slides against a rough horizontal surface, its displacement is opposite to the force of friction. The work done by the friction is negative.
(ii) When brakes are applied to a moving vehicle, the work done by the braking force is negative. This is because the braking force and the displacement act in opposite directions.
(iii) When a body is lifted, the work done by the gravitational force is negative. This is because the gravitational force acts vertically downwards while the displacement is in the vertically upward direction.
(iv) When a positive charge is moved towards another positive charge, the work done by the force of repulsion (between them) is negative because displacement s is in the opposite direction of repulsive force.
Zero work:
Work done by force is zero if the body gets displaced along a direction perpendicular to the direction of the applied force. Also, the work done is zero if F or S or both are zero.
Examples:
(i) For a body moving in a circular path, the centripetal force and displacement are perpendicular to each other. So, the work done by the centripetal force is zero.
(ii) When a coolie walks on a horizontal platform with a load on his head, he applies a force on it in the upward direction equal to its weight. The displacement of the load is along the horizontal direction. Thus, the angle between F and S is 90°. So, W = Fs cos 90° = 0 i.e., the work done by the coolie on the load is zero.