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
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.


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#