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

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 length0.65 m as in the figure below. tt coefficient of kinetic friction between the crate and rough surface is 0.355 and he exerts a constant horizontal force of 276 N on the crate. (a) Find the magnitude and direction of the net force on the crate while it is on the rough surface. magnitude direction Select (b) Find the net work done on the crate while it is on the rough surface (c) Find the speed of the crate when it reaches the end of the rough surface m/s

Explanation / Answer

(a) By F(net) = F(applied) - F(friction)
=>F(n) = 276 - µ x mg
=>F(n) = 276 - 0.355 x 92 x 9.8
=>F(n) = - 44.068 Newton [-ve indicating that it is a retarding force i.e. opposite the direction of motion]
(b) W = F(n) x s
=>W = 44.068 x 0.65 = 28.6442 J
(c) By F = ma
=>44.068 = 92 x a
=>a = 0.479 m/s^2
By v^2 = u^2 - 2as
=>v^2 = (0.865)^2 - 2 x 0.479 x 0.65
=>v = 0.125525
=>v = 0.354 m/s

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