**Work Power and Energy in Physics.**

**Work in Physics**

Whenever a force acting on a body displaces it, work is said to be done.

If a force F acting of the body displaces it by a distance s in the direction of force die work done is given by,

**W = F.s (or) W = |F||s|cosθ**

If θ < 90°, work done is positive and if θ > 90° it is negative.

Work done does not depend on the path followed and time taken.

In SI system units of work are joule and in CGS system the units of work are ergs.

1 joule = 107 erg

**Positive Work Physics :** If θ is acute (θ < 90°), work done is positive.

**Examples:
**

- When body falls freely under gravity, θ = 0, and work done is positive.
- When a lawn roller is pulled by applying a force along the handle at an acute angle, work done by applied force is (+) ve.
- When a spring is stretched or when a gas filled in a cylinder filled with moving piston is allowed to expand, work done is positive.

**Negative Work Physics : **If θ is obtuse (θ > 90°), work done is negative.

**Examples :**

- When a body is thrown up, its motion is opposed by gravity; θ between F and s is 180°.
- When a body is moved over a rough horizontal surface, the motion is opposed by the force of friction. Work done by the friction force is negative.
- When brakes are applied to a moving vehicle.
- When a positive charge is moved closer to another positive charge.

**Zero Work Physics :** If θ is right angle (θ = 90°), work done is zero.

**Examples :**

- When we fail to move a heavy stone because s-> = 0.
- Coollie carrying some load on his head on a horizontal platform θ = 90°.
- Person carrying a briefcase moves on a horizontal road.
- Tension in the string of simple pendulum is always perpendicular to the displacement of the bob, hence it is zero.

**Kinetic Energy Physics**

- Capacity of doing work is known as the energy.
- KE of the body is equal to the work done by the body before coming to rest.

**K = 1/2 mv² and W = ΔK**

- When the speed of the body is constant there is no change in kinetic energy and the work done by the resultant force is zero, e.g., in uniform circular motion.
- Work and Energy have same units.
- Kinetic energy and potential energy are called mechanical energy.

**Power**

- It is defined as the time rate of doing work.
- If an agent does work W in time t then average power is,

**P = W/t = F.s/t = F.v = |F||v|cosθ**

- It is a scalar quantity.
- SI units of power is watt and is also measured in horse power.
- 1 HP = 746 W (watt)

**Potential Energy**

- Potential energy is the energy possessed by the body by virtue of its position, configuration or any condition of stress or strain.
- Gravitational potential energy of the body at a height h = mgh
- When work is done on the system, potential energy increases and when work is done by the system, potential energy decreases.

**Examples:**

- When spring is compressed, work is done on the spring in compressing, so PE increases.
- Work is done in stretching a spring, so PE increases.
- When two dissimilar charges are brought near each other, they attract each other; work is done by the field, so PE decreases.
- Work is done by us in taking a body against gravitational field, so PE decreases.
- Air bubble rises up in water because of up-thrust, PE decreases.
- When two protons are brought towards each other they repel each other being similar charges, work is done by us in bringing them close, so PE increases.

**Law of Conservation of Energy**

It states that the total energy remains constant in any process i.e., it may neither be created nor destroyed.

**KE + PE + other forms of energy = constant**

If conservative forces are acting on a body, then,

**KE + PE = constant** i.e., the loss of PE is equal to the gain in KE.

**Einstein Relation**

According to Einstein, mass can be converted into energy and energy can be converted into mass. One can be obtained at the cost of the other.

The equivalence between mass and energy is expressed in terms of Einstein relation:

**E = mc²**

Where m is the mass that disappears, E is the energy that appears and c is the velocity of light in vacuum (c = 3 x 108; m/s).

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