An object with a mass of #2 kg# is on a ramp at an incline of #pi/12 #. If the object is being pushed up the ramp with a force of # 8 N#, what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer
Rohit Deka
Jun 3, 2018

#mu = 0.155#

Explanation:

we can write #pi/12# as 15° in degree.
enter image source here
Now please consider the image and look at the free body diagram and the forces acting on it.

#8N# force acting upwards and #mgsintheta#, #mu mg costheta# downwards. where the #mu# is coefficient of static friction, #m# is mass and #g# is accelaration due to gravity.

Thus for the object to be put,
#rArr 8N = mgsintheta + mu mgcostheta#

#rArr (8 - 2*9.8*sin15°)/(2*9.8*cos15°) = mu#

as #sin15°=0.256 and cos15°=0.998#

after calculation #mu= 0.155#

Hence coefficient of static friction is #mu = 0.155#

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