(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A smooth ring A of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley B and carries a block C of Mass M (=2m) as shown in the given figure. At a instant at the string between the ring and the pulley makes an angle [tex]\theta[/tex] with the rod, (a)Show that, if the ring slides with a speed v, the block descends with speed v cos[tex]\theta[/tex]. (b) With what acceleration will the ring start moving if the system is released from rest with [tex]\theta=~30^\circ[/tex]?

2. Relevant equations

Newtons Equations, free body diagram

3. The attempt at a solution

Well, this question happens to be from a textbook. And its a solved one too.. The solution which they have given is quite complicated! I thought I'd get a brief explanation of "why and how" over it, and yes an alternative method would be highly appreciated!

The solution, is like this (as given in the book),

Suppose in a small time interval [tex]\delta t[/tex] the ring is displaced from A to A' and the block from C to C'. Drop a perpendicular A'P from A' to AB.For small displacements A'B~ PB(I didnt get this!), since the lenght is constant (?????), we have,

AB+BC= A'B+BC'

AP+PB+BC=A'B+BC'

AP=BC'-BC=CC' (as A'B=PB)

AA'[tex]cos\theta[/tex]= CC'

or [tex]\frac{AA'cos\theta}{\delta t}=~\frac{CC'}{\delta t}[/tex]

Therefor, (velocity of the ring)[tex]cos\theta[/tex]= (velocity of the block)

Please help

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# Homework Help: Newton's Laws of motion!

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