A man of mass 50 kg is standing on one end of a stationary wooden plank resting on a frictionless surface. The mass of the plank is 10 kg, its length is 300 m and the coefficient of friction between t

Question

A man of mass 50 kg is standing on one end of a stationary wooden plank resting on a frictionless surface. The mass of the plank is 10 kg, its length is 300 m and the coefficient of friction between the man and the plank is 0.2 . Find the shortest time (in sec) in which the man can reach the other end starting from rest and stopping at the other end.

TestHub · Accepted Answer

Maximum friction on the man: f = μ m g = 0.2 × 50 × 10 = 100 N. Man's maximum acceleration a m ​ = 50 100 ​ = 2 m/s 2 ; plank's acceleration a p ​ = 10 100 ​ = 10 m/s 2 opposite. Shortest time: accelerate to the midpoint, then decelerate symmetrically. Relative acceleration = 2 + 10 = 12 m/s 2 over 150 m: 2 1 ​ ( 12 ) t 2 = 150 ⇒ t = 5 s. Total time = 2 t = 10 s

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