Question

Imagine that the above hoop is a tire. the coefficient of static friction between rubber and concrete is typically at least 0.9. what is the maximum angle θmax you could ride down without worrying about skidding? express your answer numerically, in degrees, to two significant figures.

Answer 1

The hoop is attached.

Consider that the friction force is given by:
F = μ·N
= μ·m·g·cosθ

We also know, considering the forces of the whole system, that:
F = -m·a + m·g·sinθ
and
a = (1/2)·g·sinθ

Therefore:
-(1/2)·m·g·sinθ + m·g·sinθ = μ·m·g·cosθ
(1/2)·m·g·sinθ = μ·m·g·cosθ
μ = (1/2)·m·g·sinθ / m·g·cosθ
= (1/2)·tanθ

Now, solve for θ:
θ = tan⁻¹(2·μ)
= tan⁻¹(2·0.9)
= 61°

Therefore, the maximum angle you could ride down without worrying about skidding is 61°.