An object with a mass of #7 kg# is on a ramp at an incline of #pi/12 #. If the object is being pushed up the ramp with a force of # 6 N#, what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer
Feb 2, 2016

Answer:

#mu = (6/(mgcos(pi/12)) - tan (pi/12))#

Explanation:

From FBD:
#F_i = F_f + F_(|\|) = mu F_N + mgsinalpha#
#F_i = mumgcosalpha + mgsinalpha#
#6 = mumgcos(pi/12) + mgsin(pi/12)#
Solve for #mu#
# mu = (6-mgsin(pi/12))/(mgcos(pi/12))#
# mu = (6/(mgcos(pi/12)) - tan (pi/12))#
Now pull out your calculator and voila!

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