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

Answer 1

first of all, you should know about workdone .
workdone is the dot product of force and displacement due to force applied.
e.g., $W=\vec{F}.\vec{s}$
or, $W=|\vec{F}||\vec{s}|cos\theta$, here $\theta$ is the angle between force and displacement.

case 1 :- $\theta=0$ means, force and displacement are in same direction.
then, workdone will be positive.

case 2 :- $\theta=90^{\circ}$ means, force is perpendicular upon displacement.
then, workdone = 0

case 3 : $\theta=180^{\circ}$ means , force is just opposite direction of displacement.
then, Workdone will be negative.

now come to the question.,

(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.

(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.

Answer 2

Ans.

(a) It is clear that the direction of both the force and the displacement are the same and thus the work done on it is positive.

(b) It can be noted that the displacement of the object is in an upward direction whereas, the force due to gravity is in a downward direction. Hence, the work done is negative.

(c) It can be observed that the direction of motion of the object is opposite to the direction of the frictional force. So, the work done is negative.

(d) The object which is moving in a rough horizontal plane faces the frictional force which is opposite to the direction of the motion. To maintain a uniform velocity, a uniform force is applied on the object. So, the motion of the object and the applied force are in the same direction. Thus, the work done is positive.

(e) It is noted that the direction of the bob and the resistive force of air which is acting on it are in opposite directions. Thus, the work done is negative.