A box of uniform density with a square base of side length b and height 2b sits

Question

A box of uniform density with a square base of side length b and height 2b sits on an incline. The coefficient of static friction between 'the box and the 'incline 'is µs' The angle of the incline e is increased from 0 until the box either tips over onto its side, or slides down the incline.

For what relation between µs and e does the box slide? For what relation between µs and e does the box tip?

If µs = 0.55 does the box slide down the slope or tip? At what angle of the incline does it do this?

Explanation / Answer

For sliding relation between mu_s and e is tan(e) > mu_s

for tip relation between mu_s and e is tan(e)<mu_s

for mu_s = 0.55

the angle is e = atan(0.55) = 28.8 degrees

therefore for the angles e>28.8 degrees

the box will slide

and for the angles e<28.8 degrees the box will tio to the incline

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