Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 7

7 A crate, in the form of a cube with edge lengths of 1.2 m, contains a piece of machinery; the center of mass of the crate and its contents is located 0.30 m above the crate’s geometrical center. The crate rests on a ramp that makes an angle \(\theta\) with the horizontal. As \(\theta\) is increased from zero, an angle will be reached at which the crate will either tip over or start to slide down the ramp. If the coefficient of static friction \(\mu_s\) between ramp and crate is 0.30, (a) does the crate tip or slide and (b) at what angle \(\theta\) does this occur? If \(\mu_s = 0.70\), (c) does the crate tip or slide and (d) at what angle \(\theta\) does this occur? (Hint: At the onset of tipping, where is the normal force located?)