Question

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: work done by a man in lifting a
bucket out of a well by means of a rope tied to the bucket.
work done by gravitational force in the above case, work done
by friction on a body sliding down an inclined plane,
work done by an applied force on a body moving on a rough horizontal plane with
uniform velocity, work done by the resistive force of air on a vibrating pendulum
in bringing it to rest.

Answer 1

Positive
In the given case, force and displacement are in the same direction. Hence, the sign of work done is positive. In this case, the work is done on the bucket.
Negative
In the given case, the direction of force (vertically downward) and displacement (vertically upward) are opposite to each other. Hence, the sign of work done is negative.
Negative
Since the direction offrictional force is opposite to the direction of motion, the work done by frictional force is negative in this case.
Positive

Here the body is moving on a rough horizontal plane. Frictional force opposes the motion of the body. Therefore, in order to maintain a uniform velocity, a uniform force must be applied to the body. Since the applied force acts in the direction of motion of the body, the work done is positive.

Negative
The resistive force of air acts in the direction opposite to the direction of motion of the pendulum. Hence, the work done is negative in this case.