A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.865 m/s encounters

Question

A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.865 m/s encounters a rough horizontal surface of length = 0.65 m. If the coefficient of kinetic friction between the crate and rough surface is 0.360 and he exerts a constant horizontal force of 278 N on the crate, find the following.

(a) Find the magnitude and direction of the net force on the crate while it is on the rough surface.
magnitude N
direction

(b) Find the net work done on the crate while it is on the rough surface.
J

(c) Find the speed of the crate when it reaches the end of the rough surface.
m/s

Explanation / Answer

A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.855 m/s encounters a rough horizontal surface of length script i = 0.65 m as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.360 and he exerts a constant horizontal force of 291 N on the crate, find the following. (a) By F(net) = F(applied) - F(friction) =>F(n) = 291 - µ x mg =>F(n) = 291 - 0.360 x 92 x 9.8 =>F(n) = - 33.58 Newton [-ve indicating that it is a retarding force i.e. opposite the direction of motion] (b) W = F(n) x s =>W = 33.58 x 0.65 = 21.82 J (c) By F = ma =>33.58 = 92 x a =>a = 0.37 m/s^2 By v^2 = u^2 - 2as =>v^2 = (0.855)^2 - 2 x 0.37 x 0.65 =>v = v0.25 =>v = 0.5 m/s

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