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derieve expression for kinetic and potential energy

Asked by Aniket 13th March 2015, 6:12 PM
Answered by Expert
Answer:

Hi Aniket,

Kinetic energy:

The energy possessed by an object on account of its motion is known as kinetic energy.

Consider an object of mass m, moving with initial velocity u. Let it be displaced through a distance s when a constant force F acts on it in the direction of its displacement. The work done is

begin mathsize 14px style straight W equals straight F cross times straight s end style

The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Leta be the acceleration produced.

begin mathsize 14px style straight v squared minus straight u squared equals 2 as therefore straight s equals fraction numerator straight v squared minus straight u squared over denominator 2 straight a end fraction We space also space know space that space straight F space equals space ma space Thus comma space work space done space is straight W equals ma cross times fraction numerator straight v squared minus straight u squared over denominator 2 straight a end fraction space space space equals 1 half straight m left parenthesis straight v squared minus straight u squared right parenthesis end style

begin mathsize 14px style straight W equals 1 half mv squared end style

Thus, the kinetic energy of a body is

1. Directly proportional to the mass of the body

2. Directly proportional to the square of the velocity of the body

 

Potential energy:

The energy possessed by an object on account of its position or configuration is known as 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.

The force required to raise the object is equal to the weight F = mg of the object. If it is raised to a height h, then the work done is

W=mg x h

  • This work is stored in the body as potential energy.

Work done by gravity depends on the initial and final positions and not on the path taken to raise it to the specified height.

 

 

Answered by Expert 13th March 2015, 6:26 PM
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