A train starts from rest and moves on a straight horizontal track with uniform acceleration. It covers a distance of 40 m in 4 s. A box resting on the floor of the train is observed to be just on the verge of slipping. What is the coefficient of static friction between the box and the floor of the train? (Take g = 10 m s ⁻² )

Step-by-step solution

Let the acceleration of the train be a . Using the second equation of motion: S = ut + 1 2 at^2 40 = 0 + 1 2 a (4)^2 40 = 8a a = 5 m s ⁻² For the box to be just on the verge of slipping, the pseudo force on it in the frame of the train must be equal to the limiting static friction. ma = _s mg _s = a g Substituting the values: _s = 5 10 = 0.5 Answer: 0.5