First slide

Application of Newtons laws

Question

Two monkeys M₁ and M₂ of equal mass 'm' can climb strings of a pulley arrangement as shown in figure. Find magnitude of acceleration (in m/s²) of M₁ with respect to rope so that block remains stationary. It is given that M₂is just holding the string. Assume pulley is frictionless and string is massless and inextensible.

Difficult

Solution

$\begin{array}{l} T = 5 m g \\ a_{2} = \frac{5 m g - m g}{m} = 4 g \\ T^{'} = 2 T = 10 mg \\ a_{1} = \frac{10 mg - m g}{m} = 9 g \end{array}$
Acceleration of the rope is equal to the acceleration of the moving pulley. Hence acceleration of M₁ with respect to rope
$a_{M_{1}, Rope} = 9 g - (- 2 g) = 11 g = 110 m / s^{2}$

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