# House on a Hill slope problem

## Homework Statement

A house is built on the top of a hill with a nearby 45° slope (Fig. 6-19). 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 0.67, what is the least angle through which the present slope should be reduced to prevent slippage?
(I attached an image. Hopefully it shows up - You may have to click the attachment once more after it comes in the pop-up)

## Homework Equations

f = μn
f = mg*sin ∅
n = mg*cos ∅
Current value of ∅ = 45°
μ = 0.67

## The Attempt at a Solution

I drew a free body diagram, and found that the friction force is equal and opposite that of mg*sin∅, and that the normal force was mg*cos∅.
I then set up this equation:
Net force = f - mg*sin∅
μ*n - mg*sin∅ = 0
μ*n = mgsin∅
μ*mgcos∅ = mgsin∅
(mg's cancel)
μ * cos ∅ = sin ∅
μ = tan ∅
tan-1 μ = ∅
I plugged in 0.67 for mu, and got 33.822°, which I am being told is wrong.

#### Attachments

• 16 KB Views: 456
Last edited: