As shown in the figure, monkey B is holding on to the tail of monkey A, which is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg , respectively. Given that A can tolerate a tension of 30 N in its tail, what force should it apply on the rope to carry monkey B with it? Take g = 10 m/s ^2 .

Step-by-step solution

Let a be the upward acceleration of the monkeys. For monkey B, the equation of motion is: T - m_B g = m_B a Given m_B = 2 kg and g = 10 m/s ^2 : T - 20 = 2a a = T - 20 2 For the system of monkeys A and B, the equation of motion is: F - (m_A + m_B)g = (m_A + m_B)a Given m_A = 5 kg : F - 70 = 7a Substituting the value of a : F = 70 + 7 ( T - 20 2 ) = 70 + 3.5(T - 20) To carry monkey B, the minimum upward acceleration is a = 0 , which gives the minimum tension T = 20 N . The maximum tension monkey A's tail can tolerat