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Mechanics

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19 Sep 2007 08:49:29 IST

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question from iit foundation

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a ball is dropped to a height h from the ground.if the coefficient of restitution ,the height to which the ball rises after it rebounded forthe nth time is---------------

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shashidhar sundareisan

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Joined: 15 Aug 2007

Posts: 36

19 Sep 2007 16:02:59 IST

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e^²ⁿh.
apply conservation of energy.
then apply concept of coefficient of restitution n number of times to get the ans.

Purav Master

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Joined: 9 Nov 2006

Posts: 814

19 Sep 2007 16:16:09 IST

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In case of inelastic colllision, the mechanical energy is not conserved.

If e is the coefficient of restitution, then

h (n) = H e^2n

Here h (n) is the height the ball attains fter nth collision.

So the height decreases as the ball hits the floor again and again.

The cause of this is that in case of inelastic collisions some part of the mechanical energy is converted to sound energy, heat energy, internal energy, dissipation to overcome air resistance etc.

Note that if its a perfectly elastic collision (e=1) then the height remains same after every collision. (Verify from the above formula)

However elastic collision is an ideal concept and is not possible practically.......

Hope u r clear...........

Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5153

20 Sep 2007 00:40:01 IST

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Perfect answer. It is e^(2n)*H. After every collision velocity will become e times and as maximum height is proportional to u^2 so it will become e^2 times. So in n collisions it willl be H*e^2n

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