An object with a mass of #7 kg# is on a ramp at an incline of #pi/8 #. If the object is being pushed up the ramp with a force of # 2 N#, what is the minimum coefficient of static friction needed for the object to remain put?

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Answer 1 · 2017-01-15T00:07:44

minimum friction coefficient is #0.3827# (4dp)

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For our diagram, #m=7kg#, #theta=pi/8#

If we apply Newton's Second Law up perpendicular to the plane we get:

#R-mgcostheta=0#
#:. R=7gcos(pi/8) \ \ N#

It takes #2N# to keep the object in equilibrium, so #D=2#. If we Apply Newton's Second Law down parallel to the plane we get:

# mgsin theta -D-F = 0 #
# :. F = 7gsin (pi/8) -2\ \ N#

And the friction is related to the Reaction (Normal) Force by

# F le mu R => 7gsin (pi/8) -2 le mu (7gcos(pi/8)) #
# :. mu ge (7gsin (pi/8) -2)/(7gcos(pi/8)) #
# :. mu ge 0.382656 ... #