# Energy: Kinetic Energy and Potential Energy

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

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

We know that Kinetic Energy = 1/2mv2

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/s2. 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