(a) Positive Work. Work done by a force is positive if the force acts in the direction of displacement.Then
\(W=F\times s\times cos\ 0°=F\ s\)
Examples:
(i) When a body falls freely under gravity, 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.
(b) Negative Work. Work done by a force is negative if the force acts opposite to the direction of displacement.Then
\(W=F\times s\times cos\ 180°=F\ s(-1)=-F\ s\)
Examples:
(i) When a body is lifted up, the work done by the gravitational force is negative.This is because the gravitational acts vertically downwards while the displacement is in the vertically upward direction.
(ii) When brakes are applied to a moving vehicle, the work done by the braking forces is negative.The braking force acts in the backward direction while the displacement of the vehicle is in the forward direction.

Work is said to be done whenever a force a acts on a body moves in the direction of the force.
Two conditions need to be satisfied for work to be done.These are as follows:
(i) A force should act on the body.
(ii) The body must be displaced in the direction of the applied force.
If either of the above two conditions is not satisfied, then work is not done.
Examples: We give below some situations from daily life in which work is done.
(i) Push a pebble lying on a surface.The pebble moves through some distance.Here we apply a force on the pebble and the pebble gets displaced.So, we have done work on the pebble.
(ii) We apply a force to lift a book through a height.The book rises up.We have done work in moving up the book.
(iii) A bullock is pulling a cart.The cart moves.There is a force on the cart and the cart has moved.The bullock has done work on the cart.

Here, Force(F) = 140N, Displacement (s) = 15m
Work done, W = Fs = 140 N x 15 m = 2100 J

Work is done whenever the given two conditions are satisfied:
(i) A force acts on the body.
(ii) There is a displacement of the body by the application of force in or opposite to the direction of force.
When a person holds a bundle of hay over his head, then there is no displacement in the bundle of hay. Although, force of gravity is acting on the bundle, the person is not applying any force on it. Hence, in the absence of force, work done by the person on the bundle is zero.

Here displacement AB=2m is along the horizontal direction.
The gravitational force acts on the box in the vertically downward direction i.e., perpendicular to the direction of motion.Hence the work done by the gravitational force is zero.
\(W=F\ s\ cos\ 90°=0\)

(a) No, because the centripetal force acting on the body is perpendicular to its direction of motion.
(b) No, because 40 kg weight remains at rest.
(c) No, because the force gravity on the satellite acts perpendicular to its direction of motion.

Yes, it is possible that a force is acting on a body but still the work done is zero.For example, consider a coolie carrying a load on his head across a level road.He exerts an upward force equal to the weight of the load.But the displacement of the load is in the horizontal direction.Thus the angle between force F and displacement s is \(0°\).Hence
\(W=F\ s\ cos\ 90°=0\)

Zero.
This is because the component of the force acting on a body in the direction of its displacement is zero in this case.Moreover,
\(W=F\ s\ cos\ 90°=0\)

(a) The SI unit of work is joule(J). One joule of work is said to be done when a force of one Newton displaces a body through a distance of 1 meter in its own direction.Thus,
1 joule= 1 newton x1 metre or 1J=1 Nm.
(b) Work done is a scalar quantity because it has only magnitude and no direction.

When a force F displaces a body through a distance S in the direction of the applied force, then the work done W on the body is given by the expression:
Work done = Force × Displacement
W = F x s