Energy

The capacity of doing work is known as energy.

• The sun is the biggest source of energy.
• most of the energy sources are derived from the d=sun.
• Some energy is received from nucleus of atoms, interior of the earth and the tides.

The energy possessed by an object is thus measured in terms of its capacity of doing work.

SI unit of energy is same as the work of unit that is Joule (J). Its bigger unit is kilo joule (kJ). 1 kJ = 1000 J.

There are different forms of energy:-0

• Kinetic energy
• Potential energy
• Heat energy
• Chemical energy
• Electrical energy
• Light energy
• Sound energy
• Nuclear energy

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases with its speed.

Examples of Kinetic energy:-

• A moving cricket ball
• Running water
• A moving bullet
• Flowing wind
• A moving car
• A running athelete
• A rolling stone

If an object of mass ‘m’ moving with uniform velocity ‘u’ , it is displaced through a distance ‘s’. Constant force ‘f’ acts on it in the direction of displacement. Its velocity changes from ‘u’ to ‘v’.

W = F × S………………………………………….(1)

F = m × a…………………………………………..(2)

According to the third equation of motion

v² – u² = 2as

s = ( v² – u² )/2a……………………………….(3)

W = m a × (v² – u²/2a)

W = 1/2 m ( v² – u²)

If the object is starting from its stationary position, that is u = 0, then

W = 1/2 m ( v² – 0²)

W = 1/2 mv²

Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is

E_k = 1/2m v²

Example:- An object of mass 15 kg is moving with a uniform velocity of 4 m s^-1 . What is the kinetic energy possessed by the object?

Solution:- Mass of the object (m) = 15 kg

Velocity of the object (v) = 4 m s^-1

E_k = 1/ 2 m v²

= 1/2 × 15 kg × 4 m s^-1× 4 m s^-1

= 120 J

The kinetic energy of the object is 120 J.

Potential energy

The potential energy possessed by the object is the energy present in it by virtue of its position or configuration.

Examples:-

• Water kept in dam : It can rotate turbine to generate electricity due to its position above the ground.
• Bent string of bow : Potential energy due to change of its shape released in the form of kinetic energy while shooting an arrow.

Potential energy of an object at a height:-

An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy.

The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

Consider an object of mass, m. Let it be raised through a height, h from the ground. A force is required to do this. The minimum force required to raise the object is equal to the weight of the object, mg. The object gains energy equal to the work done on it. Let the work done on the object against gravity be W. That is,

work done , W = force × displacement

= mg × h

= mgh

Thus, the potential energy of the object is E_p = mgh

Example:- Find the energy possessed by an object of mass 10kg when it is at a height of 6 m above the ground. Given g = 9.8 m s^-2.

Sol:- Mass of the object (m) = 10 kg

displacement (h) = 6 m

acceleration due to gravity (g) = 9.8 m s^-2

Potential energy = mgh

= 10 kg × 9.8 m s^-2 × 6 m

= 588 J

The potential energy is 588 J.