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

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