Question

A man pushing a crate of mass m= 92.0 kg at a speed of v=0.880m/s encounters a rough horizontal surface of length l= 0.65 m as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.356 and he exerts a constant horizontal force of 293N 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	---Select---updownin the same direction as the motion of the cratein the opposite direction as the motion of the crate

(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

Answer 1

a) By F(net) = F(applied) - F(friction)
=>F(n) = 293 - µ x mg
=>F(n) = 293 - 0.356 x 92 x 9.8
=>F(n) = - 28.30 N [-ve indicating that it is a retarding force i.e. opposite the direction of motion]

magnitude = 28.30

direction = opposite to the direction of motion

(b) W = F(n) x s

=>W = -28.3 x 0.65 = 18.39 J
(c) By F(n) = ma
=>28.30 = 92 x a
=>a = 0.31 m/s^2
By v^2 = u^2 - 2as
=>v^2 = (0.880)^2 - 2 x 0.31 x 0.65
=>v² = 0.37
=>v = 0.61 m/s