Halliday, Resnick & Walker — Force and Motion–II: Problem 76

A house is built on the top of a hill with a nearby slope at angle \(\theta = 45^{\circ}\) (Fig. 6.44). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the coefficient of static friction between two such layers is 0.5, what is the least angle \(\phi\) through which the present slope should be reduced to prevent slippage?