Answer:
[tex]\mu_{s} = 0.392[/tex]
Explanation:
Let assume that road has no inclination. The pick-up truck experiments a centripetal force as net force, whereas the crate has a centrifugal one by the Newton's 3rd Law. The crate starts moving when [tex]f = \mu_{s}\cdot N[/tex]. The crate is modelled by the following equations of equilibrium:
[tex]\Sigma F_{r} = \mu_{s}\cdot N = m_{crate}\cdot \frac{v^{2}}{R}[/tex]
[tex]\Sigma F_{n} = N - m_{crate}\cdot g = 0[/tex]
After some handling, the coefficient of static friction is determined:
[tex]\mu_{k} \cdot m_{crate} \cdot g = m_{crate}\cdot \frac{v^{2}}{R}[/tex]
[tex]\mu_{s}\cdot g = \frac{v^{2}}{R}[/tex]
[tex]\mu_{s} = \frac{v^{2}}{g\cdot R}[/tex]
[tex]\mu_{s} = \frac{(31\,\frac{m}{s} )^{2}}{(9.807\,\frac{m}{s^{2}} )\cdot (250\,m)}[/tex]
[tex]\mu_{s} = 0.392[/tex]
