Q. 14.5( 60 Votes )

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.

Answer :

Work done by a force  f on a object which give body a displacement of d

where, 
w is the work done on the object by force f
f is the force applied to the object
d is the displacement of the object after application of force  
θ is the angle between force and displacement


A. The displacement of the bucket and the force applied on the bucket by the man have the same direction i.e. θ=0. Hence, the work done by a man is positive and the work is done on the bucket.


( cos 00=1)


Hence, work done is positive.


B. The gravitational force acts downwards on the bucket. But the displacement of the bucket is upwards i.e. θ=180. Hence, the work done is negative and θ=180


( cos 1800=-1)


Hence, work done is negative.


C. Frictional force always acts opposite to the direction of motion of object i.e. θ=180. Hence, work done by frictional force is always negative. 


( cos 1800=-1)


Hence, work done is 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 i.e. θ =0. Hence, the work done by the force is positive.


( cos 00=1)


Hence, work done 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 i.e. θ =180. Hence, the work done by the resistive force is negative.


( cos 1800=-1)


Hence, work done is negative.




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