Question

A house is built on the top of a hill with a nearby slope at angle 45° slope (Figure 6-55). 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 static coefficient of friction between two such layers is 0.42, what is the least angle ϕ through which the present slope should be reduced to prevent slippage?

Answer 1

Slippage happens when the tangent of the slope angle exceeds the static coefficient of friction. Use (or derive) that fact to figure out the answer

Answer 2

A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 5.00 g coins stacked over the 12.0 cm mark, the stick is found to balance at the 43.0 cm mark. What is the mass of the meter stick?

Answer 3

Set the total moment about the knife edge equal to zero.

(meter mass)*(center distance from knife edge) = (coin mass)* (distance from knife edge)
(43 - 12)* m = 10.00 g * 7.0
Solve for m