A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.855 m/s encounters

Question

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 ? = 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 288 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.

Magntiude N

Direction: up, down, in the same direction as the motion of the crate, in 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

Explanation / Answer

here ,

a)

the net force acting on the crate ,

Fnet = 288 - 0.36 * 92 * 9.8

Fnet = -36.6 N

hence , the force acting is 36.6 N . in oposite to the direction of motion

b)

Net work done = -36.6 * 0.65

Net work done = -23.8 J

the net work done on the crate is -23.8 J

c)

Now , using work energy theorum ,

0.5 * 92 *(v^2 - .855^2) = -23.8

solving for v

v = 0.463 m/s

the speed of the crate is 0.463 m/s

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