give 4 examples of positive, negative and zero work done with diagram

#### Answers

** ZERO WORK DONE **

Work can be zero even when there is a force. The centripetal force in a uniform circular motion, for example, does zero work since the kinetic energy of the moving object doesn 't change. This is because the force is always perpendicular to the motion of the object; only the component of a force parallel to the velocity vector of an object can do work on that object. Likewise when a book sits on a table, the table does no work on the book despite exerting a force equivalent to *mg* upwards, because no energy is transferred into or out of the book.

If the table were moving upward at a constant velocity, then it will be doing work on the book, since the force of the table on the book will be acting through a distance. However, the force of gravity will be doing equal and opposite work on the book, and the net rate of work done on the book will still be zero, as evidenced by the fact that its kinetic energy remains constant throughout the process.

POSITIVE AND NEGATIVE WORK DONE We have seen the situations when the work done is zero. Work done can also be positive or negative. When 0 ^{o} <= θ < 90^{o}, work done is positive as Cos θ is positive. Work done by a force is positive if the applied force has a component in the direction of the displacement. When a body is falling down, the force of gravitation is acting in the downward direction. The displacement is also in the downward direction. Thus the work done by the gravitational force on the body is positive. Consider the same body being lifted in the upward direction. In this case, the force of gravity is acting in the downward direction. But, the displacement of the body is in the upward direction. Since the angle between the force and displacement is 180^{o}, the work done by the gravitational force on the body is negative. Note, that in this case the work done by the applied force which is lifting the body up is positive since the angle between the applied force and displacement is positive. Thus work done by the applied force which is lifting up the body is positive since the angle between the applied force and displacement is positive. Thus work done is negative when 90 ^{o} < θ <= 180^{o} as Cos θ is negative. We can also say that work done by a force is negative if the applied force has a component in a direction opposite to the displacement. Similarly, frictional force is always opposing the relative motion of the body. When a body is dragged along a rough surface, the frictional force will be acting in the direction opposite to the displacement. The angle between the frictional force and the displacement of the body will be 180 ^{o}. Thus, the work done by the frictional force will be negative. |

We explain it as follows:

1. When θ is acute (<90), cosθ is positive. Hence work done is positive.

**example:** when a body falls freely under the action of gravity.

cos0 = 1. therefore work done by the gravity on the body falling freely is +ve.

2. When θ is acute (>90), cosθ is -ve. Hence work done is -ve.

**example:** when a body is thrown up, its motion is opposed by the gravity. the angle θ b/w gravitational force and displacement is 180. cos 180 = -1, therefore work done by the gravity on a body moving upward is -ve.

3.

when, θ = 90

cos90 = 0

work done is said to be zero.

**example:** when a body tied to one end of a string is rotating in a circle, work done by the centripetal force applied along the string is zero because

θ = 90

Hope this will help you to understand the concept.

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