A box with a mass of 40.0 kg is pulled along a level floor at a constant speed by a rope that makes an angle of 20.0o with the floor as shown below. If the force on the rope is 200 N, then coefficient of sliding friction or ) between the box and the floor is:

Question

A box with a mass of 40.0 kg  is pulled along a level floor at a constant speed by a rope that makes an angle of 20.0o with the floor as shown below. If the force on the rope is 200 N, then coefficient of sliding friction   or  ) between the box and the floor is:

a)  0.58
b)  0.48
c)  0.51
d)  0.30

Henry · Answer

Fh = 200*cos20 = 187.9N.

Fv = 40*9.8 + 200*sin20,
Fv = 392 + 68.4 = 460.4N.

Since the velocity is constant, the
acceleration = 0:

Fn = ma = 0, Fn = Net force,
Fh - uFv = 0, uFv = force of friction.
187.9 - 460.4u = 0,
-460.4u = -187.9,
u = -187.9 / -460.4 = 0.408.