Work, Energy and Power

Work: If a body gets displaced when a force acts on it, work is said to be done. Work is measured by the product of force and displacement of the body along the direction of force.

If a body gets displaced by S when a force F acts on it, then the work W = F S cosθ

where θ = angle between force and displacement

If both force and displacement are in the same direction, then W = FS

⇒ If force and displacement are perpendicular to each other, W = 0 as cosθ = 0.

For example, in case of uniform circular motion work done by the centripetal force is zero.

Work is a scalar quantity and its SI unit is joule.

Energy: Capacity of doing work by a body is called its energy.

⇒ Energy is a scalar quantity and its SI unit is joule.

⇒ Energy developed in a body due to work done on it is called mechanical energy.

⇒ Mechanical energy is of two types: 1. Potential Energy 2. Kinetic Energy

Potential Energy: The capacity of doing work developed in a body due to its position or configuration is called its potential energy.

Example: 1. energy of stretched or compressed spring 2. energy of water collected at a height 3. energy of spring in a watch 4. stretched bow

PE of a body in the gravitational field of earth is mgh. hoes where m = mass, g acceleration due to gravity, h height of the body from surface of the earth.

Kinetic Energy: Energy possessed by a body due to its motion is called Kinetic Energy of the body.

If a body of mass m is moving with speed u, then kinetic 1 energy of the body is 1/2/mv²

⇒ A flying aeroplane has both potential as well as kinetic energy.

⇒ If two bodies have same kinetic energy, then the body with smaller mass will have higher momentum.

Energy can neither be created nor can be destroyed. Only energy can be transformed from one form to another form. Whenever energy is utilized in one form, equal amount of energy is produced in other form. Hence total energy of the universe always remains the same. This is called the principle of conservation of energy.

⇒ When a ball is thrown vertically upward its potential energy increases, kinetic energy decreases but the total energy remains constant.

K.E= p² /2m where p = momentum = mv 

Clearly when momentum is doubled, kinetic energy becomes four times.

Power: Rate of doing work is called power.

If an agent does W work in time t, then power of agent = W / t

SI unit of power is watt named as a respect to the scientist James Watt.

watt = joule/sec.

1 kW = 10³ watt, 1 MW = 10⁶ watt

Horse power is a practical unit of power.

1 H.P. = 746 watt.

1 watt second = 1 watt × 1 second = 1 joule.

1 watt hour (Wh) = 3600 joule

1 kilowatt hour (kWh) = 3.6 × 10⁶ joule.

W, kW, MW & H.P. are units of power.

Ws, Wh, kWh are units of work and energy.

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