The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive 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 inclined 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.

(A) Positive: The force applied by the man and the displacement of the bucket are in the same direction (upward). Therefore,the work done is positive.
$(b)$ Negative: The gravitational force acts vertically downward,while the displacement of the bucket is vertically upward. Since the angle between force and displacement is $180^{\circ}$,the work done is negative.
$(c)$ Negative: Frictional force always acts opposite to the direction of motion. Thus,the work done by friction is negative.
$(d)$ Positive: To maintain uniform velocity on a rough surface,the applied force must balance the frictional force. Since the applied force acts in the direction of motion,the work done is positive.
$(e)$ Negative: The resistive force of air acts opposite to the direction of motion of the pendulum bob at every instant. Hence,the work done is negative.