# Kinetic Energy

**Kinetic energy** is the energy of motion. An object which has motion, whether it be vertical or horizontal motion has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) of an object has, depends upon two variables: the mass (m) of the object and the speed (v) of the object.

Â

**Kinetic energy**

W = F Â´ S

F = m Â´ a

**Consider these Examples:**

Â

Â

(a) A moving cricket ball hits the stumps and knocks off the stumps.

(b) A stone thrown at a glass window breaks the glass.

(c) The rotating blades of a grinder crush the spices to a fine powder.

Â

Moving objects, therefore, can do work. An object moving faster can do more work than an identical object moving at a slower pace.

Â

All these examples show that moving objects possess energy. **'The energy that an object possesses by virtue of its motion is called kinetic energy'**. Kinetic energy of an object increases with its speed.

# Factors influencing Kinetic Energy

Kinetic energy depends upon the mass of the body. Greater the mass of the body, greater is its kinetic energy. For example, a heavy cricket ball thrown at you will hurt more than a light table-tennis ball thrown with the same speed.

Â

Kinetic energy depends upon the speed of the body. Greater the speed of the body, greater is its kinetic energy. For example, a fast moving truck crashing into a wall can cause more damage than a slow moving truck striking the same wall.

Â

How much energy is possessed by a moving object?

Earlier you learnt that a moving object can do work. So, kinetic energy of an object moving with a certain velocity is equal to the amount of work done on it to make it acquire that velocity.

Â

Consider an object of mass m moving with a uniform velocity u m/s. Let it be displaced by a constant force F acting on it, through a distance 'S'. The work done here is:

Â

W = F x S

Â

The work done on the object brings about a change in its velocity from u to v m/s. The acceleration produced on it is a. From Newtonâ€™s third equation of motion we know that

Â

v^{2 }â€“ u^{2 }= 2as or s = (v^{2 }â€“ u^{2})/ 2a

Â But F = ma.

Therefore W = (ma x v^{2 }â€“ u^{2})/ 2a

Â Â Â Â Â Â Â Â Â Or W = Â½ m (v^{2 }â€“ u^{2})

If the object is starting from rest, u = 0 m/s.Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â W = Â½ mv^{2}

From the above it is clear that work done is equal to the change in kinetic energy of the object.

Therefore E_{K} = Â½ mv^{2 }joule. This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. This means, for a two-fold increase in speed, the kinetic energy will increase by a factor of four; for a three-fold increase in speed, the kinetic energy will increase by a factor of nine; and for a four-fold increase in speed, the kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon the square of the speed. As it is often said, an equation is not merely a recipe for algebraic problem-solving, but also a guide to thinking about the relationship between quantities.

Â