## What is Power?

What is Power? The magnitude of work done by a person does not depend on time. If two people A and B complete the same task in 2 minutes and 4 minutes respectively, then A person will be said to be more powerful than B i.e. person A's strength is more than person B.

Therefore, the time rate of work done by a person is called Power. It is represented by P.

Power is a scalar sign.

We know that, work

(W) = F × s …(2)

Putting the value of equation 2 in equation 1,

P = d(Fs)/dt

P = F.ds/dt

P = F.v

P = F.vcosθ

Here θ is the angle between vector F and vector v.

### Dimensional Formula and Units of Power

We know,

Power (P) = Work (W)/Time(t)

Power (P) = [ML^{2}T^{-2}]/[T] = [ML^{2}T^{-3}]

#### What is the unit of Power?

In the SI system of power, the unit is Watt. If a person or object does 1 joule of work in 1 second, then its power is called 1 watt.

1 watt = 1 joule / sec

In the CGS method, the unit of power is arg/sec.

1 watt = 10^{7} arg / sec

Other large units of power are kilowatt (kW), megawatt (MW), and horsepower (HP).

1 Kilowatt (kW) = 103 watts

1 Megawatt (MW) = 106 watts

1 horsepower (HP) = 746 watts

## Conservative and Non-conservative Forces

### Conservative Force

**Conservative Force** is the force by which the work done in moving a body from one point to another depends only on the initial and final positions of the body, not on the path of the body.

If a body is moved from point A to point B by the APB, AQB, etc. routes, then in each case the work done by the force exerted on it is equal to

So that force is a **Conservative Force**.

The forces of gravity, static electrical force, electromagnetic force, etc. are protective forces.

#### Gravitational force is a Conservative Force

To confirm this statement, suppose that the mass of an object is m, which goes from a point P to point M at a height of h. In moving the object from point P to M, four paths are followed, which are shown in the figure.

In the image (a), an object is lifted upward against the gravitational force without acceleration.

Hence the work done against the gravitational force,

W = force × displacement

**W = mgh**

In Fig. (B), the object moves from point P to M in a circular plane with OM, so the work done

W = F×OM

F = mgsinθ

OM = h/sinθ

W = mg sinθ×( h/sinθ)

*W = mgh*

The object in Fig. (C) is supported by stairs from P to M. If the height of a ladder is h 'and the number of stairs is n, then the work done

W =mgh’×n

W = mgh

mgh = mgh'× n

**W = mgh = mgh’×n**

In Fig. (D), the object moves from point P to M by a zigzag. The weight of the object is perpendicular to any horizontal path, so the work done in horizontal displacement

W = ∑mg(∆h)

Here, ∆h = height of the short vertical path is clear from the above conditions that the work against the gravitational force between any two points or the work done by the gravitational force depends on the position of those two points and not by the object moving between them. On the chosen path.

Work done in moving the object from point P to M.

W_{1} = F × h × cosθ

F = mg, θ = 180^{o}

W_{1} = mgh cos180^{o}

**W _{1} = -mgh ...1**

Again the work done by the gravitational force from M to P,

W_{2} = Fh cosθ

F = mg, θ = 0^{o}

**W _{2} = mgh ...2**

Adding equation 1 and equation 2

W = W_{1} + W_{2}

W = -mgh + mgh W

**W = 0**

The work done by the gravitational force in the complete circle of the object is zero. Therefore, the gravitational force is a protective force.

#### Properties of Conservative Forces

- The work done in moving the body against the protective force depends only on the final and initial conditions of the body.
- The work against the protective force depends on the route joining the final and initial conditions of the body.
- All the central forces, ie the water whose direction is always towards a point or away from that point and its value depends on the distance from the point, are protective forces.
- Gravitational force, static electrostatic force, comes under a central force, ie these forces are protective forces.
- Under the influence of these forces, the work done in the entire cycle is zero when a body moves along a closed path.

### Non-conservative Force

The force by which the work done in moving a body from one point to another depends on the initial and final positions of the body as well as the path set by the body is called Non-conservative Force. Frictional force, viscous force, etc. are Non-conservative Force.

#### Properties of Non-conservative Forces

- The work done in moving the body against these forces depends on the final and initial position of the body as well as the path joining them.
- Against these forces, the work done in the entire cycle is not zero when the body moves in the closed path.

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