a.
- i. The angle for telegraph hill is 17.48⁰
- ii. The coefficient of static friction has to be no less than 0.315
b.
- i. The angle for Canton Ave. is 20.3⁰
- ii. The coefficient of static friction has to be no less than 0.37
c.
- i.The angle for Bradford Street is 22.3⁰
- ii. The coefficient of static friction has to be no less than 0.41
What is a grade?
A grade is the ratio of the vertical rise to horizontal run of a road
What is the coefficient of static friction?
The coefficient of static friction is a number which shows the amount of friction between two surfaces.
a. i. Angle for Telegraph hill
Since grade = rise/run
= tan θ
So, θ = tan⁻¹(grade)
Since grade for Telegraph hill = 31.5%
= 31.5/100
= 0.315
θ = tan⁻¹(grade)
θ = tan⁻¹(0.315)
θ = 17.48⁰
So, the angle for telegraph hill is 17.48⁰
ii. Coefficient of static friction for Telegraph hill
For no sliding the coefficient of static friction, μ ≥ tanθ
≥ tan17.48⁰
≥ 0.315
So, the coefficient of static friction has to be no less than 0.315
b. i. Angle for Canton Ave.
Since grade = rise/run
= tan θ
So, θ = tan⁻¹(grade)
Since grade for Canton Ave. = 37%
= 37/100
= 0.37
θ = tan⁻¹(grade)
θ = tan⁻¹(0.37)
θ = 20.3⁰
So, the angle for Canton Ave. is 20.3⁰
ii. Coefficient of static friction for Canton Ave.
For no sliding the coefficient of static friction, μ ≥ tanθ
≥ tan20.3⁰
≥ 0.37
So, the coefficient of static friction has to be no less than 0.37
C. i. Angle for Bradford Street
Since grade = rise/run
= tan θ
So, θ = tan⁻¹(grade)
Since grade for Bradford Street = 41%
= 41/100
= 0.41
θ = tan⁻¹(grade)
θ = tan⁻¹(0.41)
θ = 22.3⁰
So, the angle for Bradford Street is 22.3⁰
ii. Coefficient of static friction for Bradford Street
For no sliding the coefficient of static friction, μ ≥ tanθ
≥ tan22.3⁰
≥ 0.41
So, the coefficient of static friction has to be no less than 0.41
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