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In fig shown the blocks A and C are pulled down with constant velocities u.Find the acceleration of block B at the given moment.

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Asked by m.nilu 23rd July 2018, 9:32 PM
Answered by Expert
Answer:
Information about masses of blocks is not given explicitly in the question. Hence I assume masses are not same.
 
Since Blocks A and C are pulled with constant speed, tension in the strings are due to weight of blocks only.
Tensions are marked in figure.
 
we write Newton's law for block-B, based on the forces acting on it.
 
begin mathsize 12px style open parentheses T subscript A space cos theta space plus space T subscript C space cos theta space minus space m subscript B g space close parentheses space equals space m subscript B cross times a end style .................................(1)
where a is acceleration of block-B
 
By substituting the tensions in eqn.(1), we get begin mathsize 12px style a space equals space fraction numerator open parentheses m subscript A cos theta space plus m subscript C space cos theta space minus space m subscript B close parentheses cross times g over denominator m subscript B end fraction end style ...................(2)
if masses are identically same, then we get begin mathsize 12px style a space equals space open parentheses 2 space cos theta space minus 1 close parentheses cross times g end style ...............(3)
where begin mathsize 12px style cos space theta space equals space fraction numerator square root of a squared minus b squared end root over denominator a end fraction end style
Answered by Expert 27th July 2018, 4:45 PM
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