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Question

A string with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass M= 2kg attached to it at a distance of 1 m from the wall. A mass m = 0.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will the speed which the mass m will hit the wall when the mass m is released?
1143433_5c6f29358b5f48eaba52ce7761818b7f.png

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Solution

Constrained:V2cosθ=V1..............(1)
Distance traveled by m =2cosθ1
tanθ=12
cosθ=25
=51
Wall =Δk
2g(1)0.5g(51)=12×2×=V22+12×0.5×V212055+5=V22+12×0.5×V22cos2θV22=1252556V2=1252556

1209035_1143433_ans_4cb28b5200e449139cd0cc6d45445b90.png

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