Question

1. a car racing on a flat track travels at 19.5 m/s around a curve with a 48 - m radius. calculate the minimum coefficient of static friction between the tires and the road that is necessary for the car to round the curve without slipping? (μ =?)

Explanation:

Step1: Analyze the forces

The centripetal force \(F_c = \frac{mv^2}{r}\) is provided by the static frictional force \(F_f=\mu_s N\). On a flat track, \(N = mg\). So, \(\frac{mv^2}{r}=\mu_s mg\).

Step2: Solve for \(\mu_s\)

Cancel out \(m\) from both sides of the equation \(\frac{v^2}{r}=\mu_s g\). Then \(\mu_s=\frac{v^2}{rg}\). Given \(v = 19.5\space m/s\), \(r=48\space m\), and \(g = 9.8\space m/s^2\). Substitute the values: \(\mu_s=\frac{(19.5)^2}{48\times9.8}\).
Calculate \((19.5)^2=380.25\), and \(48\times9.8 = 470.4\). Then \(\mu_s=\frac{380.25}{470.4}\approx0.81\).

Answer:

0.81