The sign of work done by a force on a body is important to understand. State carefully if the following quantities are poisitve or negative :
(a) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
(b) Work done by gravitational force in the above case. (c ) Work done by friction on a body sliding down an iniclined plane.
(d) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
(e) Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

Explanation

Work done `W=vecF. vecs=Fs cos theta` where `theta` is smaller angle between force `vec F` and displacement `vec s`.
(a) To lift the bucket, force equal to weight of bucket has to be applied vertically upwards and the bucket moves along the same direction i.e., `theta=0^(@)` therefore `W=F s cos 0^(@)=F s.` It si positive.
(b) The bucket moves in a direction opposite to the gravitational force which acts vertically downwards.
`:. theta=180^(@), W=F s cos 180^(@)=-Fs.` It is negative.
(c) Friction always opposes the relative motion `:. theta =180^(@), W=F s cos 180^(@)=-Fs`. It is negative.
(d) As the body moves along the direction of applied force `theta=0^(@), :. W=F s cos 0^(@)=Fs.`. It is positive.
(e) The direction of resistive force is opposite to the direction of motion of the bob, i.e., `theta=180^(@).`. Hence, work done, in this case, is negative.