An object with a mass of #5 kg# is on a ramp at an incline of #pi/12 #. 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?

1 Answer
Apr 21, 2016

Lets consider the total force on the object:

  1. #2N# up the slant.
  2. #mgsin(pi/12) ~~ 12.68 N# downwards.

Hence the total force is #10.68N# downwards.

Now the force of friction is given as #mumgcostheta# which in this case simplifies to #~47.33mu N#

so #mu = 10.68/47.33 ~~ 0.23#

Note, had there not been the extra force, #mu = tantheta#