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**Work**

The intuitive meaning of work is quite different from the scientific definition of work. In everyday activity, the term 'work' is used equally for mental work and for physical work (involving muscular force).__Examples:__

- You may
**read a book or exert yourself mentally**in thinking about a simple or difficult problem. - You might be
**holding a weight without moving**. - You may be
**carrying a load and moving with uniform velocity**. - You may be
**trying hard to move a huge rock that does not move**despite your best efforts, though you may get completely exhausted in the process.

In all these cases, according to scientific definition, **you are not doing any work.**

**➢ The Scientific Conception of Work**

- In physics, the term work is used in a special technical sense and has a much more precise definition.
__Examples:__

- When a
**box is pushed on a floor by applying a force**and it moves through some distance, work is said to be done. In this case, the applied force displaces the box. - When
**we pull a trolley by applying a force and it moves**through some distance, work is again said to be done. - When
**we lift a box through a height, we have to apply force**. In this case, the applied force does work in lifting the box.

__From all the examples given above, it follows that work is done if:__

- Force is applied on the object.
- The object is displaced from its original position.

Note:No work is said to be done if any of the two conditions is not satisfied.

**➢ Work: When Constant Force is Acting in the Direction of Displacement**

- If a body, A is kept on a smooth horizontal surface, and a force F is applied as shown.
- This force acts on the body for some time during which the displacement of the body is s.
- In such a case, work is defined as follows,
**work done by a force on a body is the product of force and displacement of the body in the direction of the force.**

- Work = Force × Displacement i.e. W = F × s.
- Work is a scalar quantity, i.e. it has no sense of direction.

**➢ Unit of Work**

__In cgs system:__

- Unit of work =
**erg.** - When a force of 1N acts on an object and the object moves a distance of 1cm in the direction of the force, the work done by the force is 1erg.
- 1erg = 1 dyne × 1 cm.

__In SI system:__

- Unit of work =
**joule(J).** - When a force of 1N acts on an object and the object moves a distance of 1m in the direction of the force, the work done by the force is 1J.
- 1J = 1 N x 1 m.

Question 1:The unit of work in S.I. units is

Definition of One JouleWhen F = 1N, s = 1m, then W = 1J.

If a displacement of 1m is produced by a force of 1N acting in the direction of displacement then the work done by the force is 1J.

1J= 1 N x 1 m = 105 dyne × 102 cm = 107 erg

Let us consider body A lying on a smooth horizontal surface. A constant force F acts at an angle θ to the horizontal. The body is displaced through a distance in the horizontal direction.

**➢ Work: When a Constant Force is Acting at an Angle to the Displacement**

- Here the complete force F is not responsible to displace the body. A part of the force acting in the direction of displacement is responsible for displacing the body. This horizontal part is F cos θ.
- Work done in this case is defined as 'Work done by a constant force acting at an angle to the displacement is the
**product of the component of force in the direction of displacement and the displacement of the body**'. - Work = Component of force in the direction of displacement x Displacement,

i.e. W = (F cos θ ) × s ⇒**W = F s cos θ.** - Work done is maximum when a force acts in the direction of displacement.

__Case-1:__

**Work done is positive when θ is acute**. This is because cos θ is positive.- Work done is maximum when θ = 0°. This is because the maximum value of cos θ = 1.

This happens when a force acts in the direction of displacement.

Question 2:A gardener pushes a lawn roller through a distance of 20m. If he applies a force of 20kg weight in a direction inclined at 60° to the ground, find the work done by him. (g=9.8m/s^{2})

__Case-2:__

- When the angle between force and displacement is 90°,

i.e. when θ = 90°, then cos 90° = 0. - In this case,
**work done is zero**.

- Work done by
**centripetal force.**

When a stone is whirled in a horizontal circle, the centripetal force acts at 90° to the displacement. Therefore, work done by the centripetal force is zero. - Work done by
**coolie.**

When a coolie moves on a horizontal surface, he applies a force on the load kept on his head in the vertically upward direction. Therefore, θ = 90°. Therefore, work done by the force applied by coolie is zero. - The motion of the
**Earth around the Sun.**

Work done by the centripetal force (which is the gravitational pull of the sun on earth) acting on earth is zero. Because centripetal force is perpendicular to the displacement. [Remember the displacement is always tangential and centripetal force is always radially inward. The angle between radius and tangent is 90°].

Work done in various situation

Question 3:For a body moving in a circular path, the work done by the centripetal force is ___________

__Case-3:__

When the angle between force and displacement is 180°,

i.e. when θ =180° then cos 180° = -1.

In this case,** work done is negative.****Example: **A block A is pushed by the force F and displaced through a distance s.

- Work done by the applied force,

W = F × s × cos 0° = Fs. - Work done by frictional force,

W = f × s × cos 180° = – fs.

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