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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