Optimal Slope Angle for Hilltop House Stability

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In summary, the conversation discusses an engineering study regarding a slope on a hill and the potential for slippage due to the angle of the slope. The question asks for the least angle by which the current slope should be reduced to prevent slippage, given a static coefficient of friction between layers of 0.67. The conversation also includes a diagram and equations to solve for the angle, which is found to be 33.822°.
  • #1
majormaaz
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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.

Can somebody please help me? I have one more submission left.
 

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  • #2
Looks like you solved for the correct angle to me.
Are they asking how much the angle should be reduced by? Or reduced to?
 

What is the "House on a Hill slope problem"?

The "House on a Hill slope problem" is a common scenario used in physics and engineering to represent a house located on a hill slope. This problem involves analyzing the forces acting on the house and determining its stability.

What are the main factors that contribute to the stability of a house on a hill slope?

The main factors that contribute to the stability of a house on a hill slope are the weight of the house, the angle of the slope, and the distribution of the weight of the house across the slope. Other factors such as the type of soil and potential external forces also play a role.

How is the stability of a house on a hill slope determined?

The stability of a house on a hill slope is determined by calculating the forces acting on the house, including the weight of the house, the force of gravity, and any external forces such as wind or seismic activity. These forces are then compared to the resistance of the house's foundation and the friction between the house and the slope.

What are some potential solutions to improve the stability of a house on a hill slope?

Some potential solutions to improve the stability of a house on a hill slope include reinforcing the foundation and structure of the house, implementing drainage systems to prevent water buildup, and adjusting the distribution of weight within the house to better distribute the forces acting on it.

How does the angle of the slope affect the stability of a house?

The angle of the slope is a crucial factor in determining the stability of a house. A steeper slope will result in a greater force of gravity acting on the house, making it more susceptible to sliding or toppling. Additionally, a steeper slope may also lead to increased water runoff and soil erosion, further compromising the stability of the house.

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