An object with a mass of 15 kg is on a ramp at an incline of pi/8 . If the object is being pushed up the ramp with a force of 9 N, what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer
MM
Apr 1, 2017

The coefficient of static friction is obtained from the ratio of the Normal force to the force parallel to the incline, in this case 9N in a direction up the incline.

Explanation:

The forces involved are:

  • force of gravity on the 15 kg block, which is 15kg * 9.8ms^-2 = 147N
  • Normal force on the block perpendicular to the incline, which is 147*cos (pi/6) = 147N
  • force on the block parallel to the incline which is 147*sin(pi/6) = 1.34N
    If there is a force of 9N pushing up the incline, and a parallel force of 1.34 N in the opposite direction, then the net force up the incline is 7.66 N.
    The coefficient of static friction therefore, is 7.66 / 147 = 0.52
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