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Mechanics Problem

Mechanics Problem

by Rahul Sharma -
Number of replies: 2
All the surfaces shown in figure are assumed to be frictionless. The block of mass m slides on the prism of mass M which in turn slides backward on the horizontal surface. Find the acceleration of the smaller block with respect to the prism.
 
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Well I found out acceleration of both the blocks and then considered a pseudo force on the smaller block since we have to find acceleration with respect to the accelerating prism. I got two accelerations acting on smaller block m making an angle theta and then I took resultant of the two accelerations but ended up with the wrong answer, someone please help!
In reply to Rahul Sharma

Re: Mechanics Problem

by lokesh sardana -

yes rahul, you are going in right direction.........<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

we have to consider pseudo force on smaller block.Let mass of prism : M,

<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" />mass of block:m,

normal rxn between them:N,

acc.of prism w.r.t ground:A

acc.of block w.r.t prism:ar

now,first we will equate forces on prism.

Nsin@=MA        ----------(1)

now, consider forces on block,

mar==mgsin@ + mAcos@  -----------(2)

N=mgcos@ - mAsin@ -----------(3)

solve (1),(2),(3) to get your answer which is

ar =gsin@(M+m)/{M+m(sin@)2}