A monkey of mass 15 kg is holding a vertical rope. The rope will not break when a mass of 20 kg is s

Question

A monkey of mass 15 kg is holding a vertical rope. The rope will not break when a mass of 20 kg is suspended from it but will break if the mass exceeds 20 kg. What is the maximum acceleration with which the monkey can climb up along the rope? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

Professor PC Thomas Classes · Answer

The breaking tension $T_{max} = 20g = 200 \mathrm{~N}$. The equation of motion for climbing up is $T - mg = ma$. To find maximum acceleration, $T = T_{max}$. $200 - 15 	imes 10 = 15a \implies 200 - 150 = 15a \implies 50 = 15a \implies a = 50 / 15 = 10 / 3 \mathrm{~m/s}^2$.