Question 3(ii) A disc of mass m slides on a smooth horizontal table and is attac

Question

Question 3(ii)

A disc of mass m slides on a smooth horizontal table and is attached to a string that passes through a hole in the table.

1. If the mass moves in a circular path of radius ro with transverse velocity Vo what is the tension T.

2. Starting from the initial conditions described in part 1, the tension is increased in such a way that the string is pulled through the hole at a constant rate until r=1/2ro, Determine T as a function of r as this is taking place.

3. How much work is done on the mass in pulling the string through the hole as described in part 2.

Explanation / Answer

>> As, Tension in String is due to the Centrifugal Force acting on the ball

As, Centrifugal Force at the instant when radius = Ro and Transverse Velocity = Vo

=> Tension in String = mVo2/Ro

>> Now, at radius r,

Tension, T = mVo2/r

and, at r = Ro/2,

Tension, T = 2*mVo2/Ro

>> As, Disc is moved by Ro - Ro/2 = Ro/2, along the direction of Tension Force

So, Work Done = int [ (mVo2/r )*dr ] = mVo2* ln[(Ro/2)/Ro] = - 0.693*mVo2 .......ANSWER....

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