What is the minimum possible value of the coefficient of static friction?

Question

and how you find it with given N crate of apples sitting on a ramp at x degree?

Answer 1

I am assuming that the minimum is to prevent the crate from slipping.

A fre-body diagram of the crate has gravity pulling it downward that has a component perpendicular to the ramp, p:
Cos(x)*m*g=p
and parallel,h:
Sin(x)*m*g=h

The perpendicular is the Normal force, so friction must be greater than the parallel force:
u*p>h
where u is the coefficient

so
u>h/p
u>(Sin(x)*m*g)/(Cos(x)*m*g)
or
u>Tan(x)

j

Answer 2

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