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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 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 290 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. (c) Find the speed of the crate when it reaches the end of the rough surface.

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onyebuchinnaji

(a) The magnitude of the net force on the crate is -26.46 N.

(b) The net work done on the crate while it is on the rough surface is -17.2 J.

(c) The speed of the crate when it reaches the end of the rough surface is 0.61 m/s.

Magnitude of net force on the crate

The magnitude of the net force on the crate is calculated as follows;

F(net) = F - Ff

where;

  • Ff is frictional force

F(net) = F - μmg

F(net) = 290  - (0.351)(92)(9.8)

F(net) = -26.46 N

Net work done on the crate

W = Fd

W = -26.46 x 0.65 = - 17.2 J

Speed of the crate

acceleration of the crate, a = F/m

                                          a = -26.46/92

                                          a = -0.288 m/s²

v² = u² + 2as

v² = 0.865² + (2)(-0.288)(0.65)

v² = 0.374

v = 0.61 m/s

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