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. The displacement of the bucket and the force applied on the bucket by the man have the same direction. Hence, the work done by a man is positive and the work is done on the bucket.
B. The gravitational force acts downwards on the bucket. But the displacement of the bucket is upwards. Hence, the work done is negative.
C. Frictional force always acts opposite to the direction of motion of object. Hence, work done by frictional force is always negative.
D. In this case, frictional force acts on the body due to the roughness of the horizontal plane in a direction opposite to the direction of motion. To obtain a uniform velocity, a uniform force must be applied in the direction of motion. Hence, the work done by the force is positive.
E. The resistive force always acts in the direction opposite to that of the motion of pendulum to bring the pendulum to rest. Hence, the work done by the resistive force is negative.
NOTE: Work done by a force 
that causes a displacement 
is given by
⇒ 
where, θ is the angle between force and displacement
If displacement is along the applied force, then
⇒ 
(∵ cos 00=1)
Hence, work done is positive.
If displacement is in the direction opposite to that of applied force, then
(∵ cos 1800=-1)
Hence, work done is negative.