Abox with a mass of m = 50 kg is pulled along a horizontal surface by a force F-

Question

Abox with a mass of m = 50 kg is pulled along a horizontal surface by a force F-200 N applied at an angle of above the horizontal. The coefficient of kinetic friction between the box and surface is p-0.30, and the box is pulled a distance ofd = 10 m, with an initial velocity of vo = 5 m/s. 60. 1. How much work is done by the pulling force F? 13 points) a. b. How much work is done by friction? 13 points c. What is the combined work done by both the normal force and gravity? |2 points d. Using the workesnerry theorem, determine the final velocity (v of the box. 13 points

Explanation / Answer

here,

mass , m = 50 kg

d = 10 m , v0 = 5 m/s

applied force , F = 200 N

uk = 0.3

a)

the work done by the pulling force , Wp = F * d * cos(theta)

Wp = 200 * 10 * cos(60) J

Wp = 1000 J

b)

frictional force , ff = uk * ( m * g - F * sin(theta))

the work done by friction , Wff = ff * d * cos(180)

Wff = - uk * ( m * g - F * sin(theta)) * d

Wff = - 0.3 * ( 50 * 9.81 - 200 * sin(60)) * 10

Wff = - 951.9 J

c)

the combined work done by both the normal force and gravity is zero as theta = 90 degree

d)

using work energy theorm

work done = kinetic energy gained

Wp + Wff = 0.5 * m* ( v^2 - v0^2)

1000 - 951.9 = 0.5 * 50 * ( v^2 - 5^2)

v = 5.5 m/s

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