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 0^{0}=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 180^{0}=-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 180^{0}=-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 0^{0}=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 180^{0}=-1)

Hence, work done is negative.

Rate this question :

The kinetic energy of a particle continuously increases with time.

HC Verma - Concepts of Physics Part 1Which of the diagrams shown in Fig. 6.7 represents variation of total mechanical energy of a pendulum oscillating in air as function of time?

Physics - ExemplarA smooth sphere of radius R is made to translate in a straight line with a constant acceleration α. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle θ it slides.

HC Verma - Concepts of Physics Part 1The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity where l is the length of the pendulum. Find the tension in the string when (a) the string is horizontal, (b) the bob is at its highest point and (c) the string makes an angle of 60^{o} with the upward vertical.