Work, Energy and Power

Work, Energy and Power

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 the case of uniform circular motion work done by the centripetal force is zero.

Work is a scalar quantity, and its SI unit is joules.

Energy

The capacity of doing work by a body is called its energy.

• Energy is a scalar quantity and its SI unit is joules.

• 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.

Examples:

1. Energy of a stretched or compressed spring

2. Energy of water collected at a height

3. Energy of spring in a watch

4. Stretched bow

Potential energy of a body in the gravitational field of earth is:

PE = mgh

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 the kinetic energy of the body.

If a body of mass m is moving with speed v, then the kinetic energy of the body is:

KE = ½ mv²

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

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

Principle of Conservation of Energy

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

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

Some Equipment Used to Transform Energy

Relation between Momentum and Kinetic Energy

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

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

• 1 kW = 10³ watts

• 1 MW = 10⁶ watts

• 1 H.P. = 746 watts (Horsepower is a practical unit of power.)

Work and energy units:

• 1 watt-second = 1 joule

• 1 watt-hour (Wh) = 3600 joules

• 1 kilowatt-hour (kWh) = 3.6 × 10⁶ joules

Thus, W, kW, MW, and HP are units of power, while Ws, Wh, and kWh are units of work and energy.

Final Thoughts

Work, energy, and power are concepts we use every day, often without realizing it. Work happens when a force causes displacement, like pushing a cart or lifting a bag. The amount of work depends on the force, distance moved, and the angle between them.

Energy is the capacity to do work. It can exist as potential energy (stored due to position, like water in a dam) or kinetic energy (energy of motion, like a moving car). A flying airplane, for example, has both.

The principle of conservation of energy tells us energy is never destroyed—it only changes form, like in a bulb where electrical energy turns into light and heat. Different devices around us transform energy daily: dynamos turn mechanical energy into electricity, solar cells capture sunlight, and motors convert electricity into motion.

Power is the rate of doing work. It’s measured in watts, kilowatts, or horsepower—terms we even see on appliances at home.