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psykatic
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Homework Statement
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]?
Homework Equations
Newtons Equations, free body diagram
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 length 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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