**Energy : If a person can do a lot of work we can say that the person has a lot of energy**

- Thus Energy is the ability to do work
**Remember the amount of energy possessed is equal to the amount of work done**- So Work Done = Energy Consumed
**Energy is a scalar quantity**

### Different Forms of energy

**Kinetic Energy**– Kinetic energy is the energy stored in something that is moving. For example, you can also feel kinetic energy when a running friend runs into you. This energy can be transferred easily, as in when your friend knocks you down (moves you).**Potential Energy**– This is the energy that is stored in objects within force fields. Fields of force can include gravity or elastic force. So when an apple is hanging high in a tree, it holds potential energy – as soon as the stem breaks, its potential energy will change to kinetic energy and it will fall to the ground.**Nuclear Energy****Electric Energy****Magnetic Energy****Chemical Energy****Thermal Energy**

**Kinetic Energy** –

Kinetic energy is the energy stored in something that is moving. For example, you can also feel kinetic energy when a running friend runs into you. This energy can be transferred easily, as in when your friend knocks you down (moves you).

By definition The energy of a body due to its motion is called Kinetic Energy

Example- A moving Cricket Ball Hitting the Stumps

Runners Running on Field posses Kinetic Energy

### Formula For Kinetic Energy Derivation

From equations of motion, the relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is

But from Newton’s second law of motion F = m a.

work done by the force, F is written as the following:

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

From work and energy theorem, work done is equal to the change in the kinetic energy of the object.

w = (1/2) mv ^{2}

If u = 0, the work done will be,

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

K.E = (1/2) mv ^{2}

- It is Clear that Kinetic energy increases in proportion to its mass
- Also Kinetic Energy varies as the square of the velocity of the body
**You can say that A heavy body with large velocity will do more work than a less heavy body with less velocity****This is the reason blacksmith uses heavier hammer than used by a gold smith**

**Examples based on what we just learnt**

**Calculate the kinetic energy of a body of mass 2kg and moving with a velocity 5m/s**

We know that Kinetic Energy = 1/2mv^{2}

M= 2kg

V= 5m/s

k.e = 2 X 5 X 5 = 25 Joule

**Example 2**

**How much work should be done on a bicycle of mass 25 kg to increase its speed from 4m/s to 6m/s**

As the work done is equal to change in kinetic energy .

**in the first case**

mass = 25 kg

speed = 4m/s

kinetic energy = 1/2 X25 X 4 X 4 = 200 J

in the second case

mass = 25 kg

speed = 6m/s

kinetic energy = 1/2 X25 X 6 X 6 = 450 J

work done = change in Kinetic energy = 450- 200= 250 joule

3. Two bodies of Equal masses move with uniform velocity v and 3v respectively. find the ratio of their Kinetic Energy.

Ans. 1:9

4.**How much work should be done on a bicycle of mass 30 kg to increase its speed from 5 m/s to 9 m/s. (ignore the air resistance and friction) .**

Ans 840 Joule

**Potential energy**

**The energy of a body due to its position or change in shape is called potential energy**- Suppose a brick lying on a ground . it has no energy stored in it .
- when you lift the block against the force of gravity, some work is done. That work is stored in the form of potential energy

**Mathematically Potential energy = M X g X h**

**Example**

**If acceleration due to gravity is 10 m/s ^{2}. What will the potential energy of a body of mass 5 Kg kept at a height of 5 metre**

Here mass= 5kg

Acceleration due to gravity = 10 m/s2

Height = 5 m

So potential energy = M X g X h

=5 X 10 X 5 = 250 Joule

**Q. A bag of weight 400kg .Upto how much height It should be raised so that the potential energy becomes 19600 joule.**

19600= 400X9.8Xh

h= 50 m.

**A body can have both kinetic energy and potential energy**