Find the mass M of the hanging block in figure (5−E16) that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

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Solution

The free-body diagram of the system is shown below:

Block ‘m’ will have the same acceleration as that of M', as it does not slip over M'.

From the free body diagrams,
T + Ma – Mg = 0 ...(i)
T – M'a – Rsinθ = 0 ...(ii)

Rsinθ – ma = 0
Rcosθ – mg = 0

Eliminating T, R and a from the above equations, we get:
$M = \frac{M' + m}{\cot θ - 1}$

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Find the mass M of the hanging block in figure (5−E16) that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light. Figure

Find the mass M of the hanging block in figure (5−E16) that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

Figure