A monkey of mass 15 kg climbs a rope having one end fixed to the ceiling. What force should it apply to the rope to ascend with an acceleration of 1 m/s ^2 ? Furthermore, if the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling? (Assume g = 10 m/s ^2 )

Step-by-step solution

Let T be the tension in the rope, which is equal to the force applied by the monkey. The equation of motion for the monkey moving upwards with acceleration a is given by T - mg = ma T = m(g + a) Substituting m = 15 kg , g = 10 m/s ^2 , and a = 1 m/s ^2 : T = 15(10 + 1) = 165 N To find the time taken to reach the ceiling, use the kinematic equation: s = ut + 1 2 at^2 Given s = 5 m , u = 0 , and a = 1 m/s ^2 : 5 = 0 + 1 2 (1)t^2 t^2 = 10 t = 10 s