A car travels around an unbanked curve at 17 m/s. If the static friction coefficient between the tires and the road is 0.45, what is the minimum radius curve that the car can take at this speed without slipping?
A) 65 m
B) 3.9 m
C) 15 m
D) 8.1 m

Question

Quizplus · Accepted Answer

The minimum radius of the curve that the car can take without slipping can be found using the formula for centripetal force, $F = \frac{mv^2}{r}$, where $F$ is the force of friction, $m$ is the mass of the car, $v$ is the velocity, and $r$ is the radius of the curve. The force of friction is also given by $F = \mu mg$, where $\mu$ is the coefficient of friction, and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting these two expressions for $F$ equal to each other and solving for $r$ gives $r = \frac{v^2}{\mu g}$. Substituting $v = 17 m/s$, $\mu = 0.45$, and $g = 9.8 m/s^2$ into this formula yields $r = \frac{(17)^2}{0.45 \times 9.8} \approx 65 m$.

A Car Travels Around an Unbanked Curve at 17 M/s