Uniform circular motion: A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?
A) 9.25 m/s
B) 23.6 m/s
C) 34.3 m/s
D) 35.0 m/s
E) 18.5 m/s

Question

Quizplus · Accepted Answer

The car will begin to skid sideways when the centripetal force required to keep the car moving in a circle exceeds the maximum static friction force. The maximum static friction force can be calculated using the formula $f_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. For a car of mass $m$ on a horizontal surface, the normal force $N$ equals the weight of the car, $mg$, where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). The centripetal force required for circular motion is given by $F_c = \frac{mv^2}{r}$, where $v$ is the velocity of the car and $r$ is the radius of the curve.Setting the maximum static friction force equal to the required centripetal force gives:$$\mu_s mg = \frac{mv^2}{r}$$Solving for $v$, we get:$$v = \sqrt{\mu_s g r}$$Substituting the given values ($\mu_s = 0.350$, $g = 9.8 \, \text{m/s}^2$, and $r = 100 \, \text{m}$):$$v = \sqrt{0.350 \times 9.8 \times 100} \approx 18.5 \, \text{m/s}$$Therefore, the car will begin to skid sideways at a speed of approximately 18.5 m/s.

Uniform Circular Motion: a 1000-Kg Car Is Slowly Picking Up