A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.860 m/s encounters

Question

A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.860 m/s encounters a rough horizontal surface of length = 0.65 m

as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.351 and he exerts a constant horizontal force of 293 N on the crate.

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

(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

given data

m = 92.0 kg
v = 0.860 m/s
= 0.65 m
coefficient of kinetic friction=0.351
force of 293 N

A) By F(net) = F(applied) - F(friction)
=>F(n) = 293 - µ x mg
=>F(n) = 293 - 0.351 x 92 x 9.8
=>F(n) = - 23.46 Newton [-ve indicating that it is a retarding force i.e. opposite the direction of motion]
(b) W = F(n) x s
=>W = 23.46*0.65 = 15.25 J
(c) By F = ma
=>23.46 = 92 x a
=>a = 0.255 m/s^2
By v^2 = u^2 - 2as
=>v^2 = (0.860)^2 - 2 x 0.255 x 0.65
=>v = 0.6388 m/s

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