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?
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#