A man pushing a crate of mass

m = 92.0 kg

at a speed of

v = 0.845 m/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 0.351 and he exerts a constant horizontal force of 280 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_N

What is the direction?

1. Opposite as the motion of the crate

2. Same 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

(a) The magnitude and direction of the net force on the crate while it is on the rough surface is 36.46 N, opposite as the motion of the crate.

(b) The net work done on the crate while it is on the rough surface is 23.7 J.

(c) The speed of the crate when it reaches the end of the rough surface is 0.45 m/s.

Magnitude of net force on the crate

F(net) = F - μFf

F(net) = 280 - 0.351(92 x 9.8)

F(net) = -36.46 N

Net work done on the crate

W = F(net) x L

W = -36.46 x 0.65

W = - 23.7 J

Acceleration of the crate

a = F(net)/m

a = -36.46/92

a = - 0.396 m/s²

Speed of the crate

v² = u² + 2as

v² = 0.845² + 2(-0.396)(0.65)

v² = 0.199

v = √0.199

v = 0.45 m/s

Thus, the magnitude and direction of the net force on the crate while it is on the rough surface is 36.46 N, opposite as the motion of the crate.

The net work done on the crate while it is on the rough surface is 23.7 J.

The speed of the crate when it reaches the end of the rough surface is 0.45 m/s.

Learn more about work done here: https://brainly.com/question/8119756

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