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Question
Find the mass M of the hanging block in figure whic will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the string and the pulleys are light.
Find the mass M of the hanging block in figure whic will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the string and the pulleys are light.
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Solution
Free body diagram
The block m does not slip over M'
From figure (i) , T - N sin θ=M′a ...(i)
From figure (ii) , N cos θ=Mg ....(ii)
N sin θ=Mg ....(iii)
From figure (iii), Mg - T =Ma ....(iv)
From equations (i) and (iv)
Mg−N sin θ=(M′+M)a
From equation (ii),
Mg−Mg tan θ=(M′+M)a
and a = g tan θ
Mg−Mg tan θ=(M′+M)g tan θ
∴M=M′+Mcot θ−1
Free body diagram
The block m does not slip over M'
From figure (i) , T - N sin θ=M′a ...(i)
From figure (ii) , N cos θ=Mg ....(ii)
N sin θ=Mg ....(iii)
From figure (iii), Mg - T =Ma ....(iv)
From equations (i) and (iv)
Mg−N sin θ=(M′+M)a
From equation (ii),
Mg−Mg tan θ=(M′+M)a
and a = g tan θ
Mg−Mg tan θ=(M′+M)g tan θ
∴M=M′+Mcot θ−1
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