The question with a diagram is in the picture. Ignore the writing Two people pus

Question

The question with a diagram is in the picture.

Ignore the writing

Two people push on a box with a mass of 40.0 kg, shown here as viewed from above. Force F1 has a magnitude of 120.0 N and a direction of 34.0 degree as measured from the x axis. Force F2 has a magnitude that is unknown, and is directed an angle of - 20.0 degree from the x-axis, The box starts from rest and moves a distance of 50.0 meters along the x axis in 8.00 seconds. Find the magnitude of force f2 and also find the coefficient of kinetic friction between the box and the floor.

Explanation / Answer

here ,

as the magnitude of net force in y-direction is zero

F1 * sin(34) - F2*sin(20) = 0

120 * sin(34) - F2 * sin(20) = 0

F2 = 196.2 N

the magnitude of force F2 is 196.2 N

Now, Using second equation of motion ,

d = 0.5at^2

50 = 0.5 * a*8^2

a = 1.56 m/s^2

Now, using second law of motion ,

ma = F1*cos(34) + F2*cos(20) - f

40 * 1.56 = 120 * cos(34) + 196.2 * cos(20) - f

f = 221.35 N

as f = uk*mg

221.35 = uk*40*9.8

uk = 0.565

the kinetic coefficent of kinetic friction is 0.565

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