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Two smooth blocks of masses m and m' connected by a light inextensible strings are moving on a smooth wedge of mass M. If a force F acts on the wedge the blocks do not slide relative to the wedge. Find the (a) acceleration of the wedge and (b) value of F.

Text Solution

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The force acting on the block m and m' parallel to the surface in contact are given as `mA larr, t rarr, m'g darr`, and `T uarr`.

Force equation relative to M: since `a_(mM)-a_(0)=0`
for `m:T=ma`...(i)
for `m':T=m'g` ...(ii)
From Eq,(i) and (ii) `A=(m')/(m) g`
(b) Force equation on system `'M+m+m'`
`Sigma F_(x)=ma_(x)`
`F=MA+mA+m'A`
`=(M+m+m')A`
`(M+m+m')(m')/(m)g`.
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