An object with a mass of $5 k g$ $5 kg$ is on a ramp at an incline of $\frac{π}{12}$ $pi/12$ . If the object is being pushed up the ramp with a force of $2 N$ $2 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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Answer 1 · 2016-04-21T16:42:40

Lets consider the total force on the object:

Hence the total force is $10.68 N$ $10.68N$ downwards.

Now the force of friction is given as $μ m g cos θ$ $mumgcostheta$ which in this case simplifies to $~ 47.33 μ N$ $~47.33mu N$

so $μ = \frac{10.68}{47.33} \approx 0.23$ $mu = 10.68/47.33 ~~ 0.23$

Note, had there not been the extra force, $μ = tan θ$ $mu = tantheta$

An object with a mass of 5 kg5kg5 kg is on a ramp at an incline of pi/12 π12pi/12 . If the object is being pushed up the ramp with a force of 2 N2N 2 N, what is the minimum coefficient of static friction needed for the object to remain put?