A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m.The coefficient of static friction between the tires and the road is 0.35.At what speed will the car begin to skid sideways?
A)9.3 m/s
B)24 m/s
C)34 m/s
D)35 m/s
E)19 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 $f_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. For a car on a horizontal surface, the normal force equals the weight of the car, $N = mg$, where $m$ is the mass of the car and $g$ 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 ($\mu_s = 0.35$, $g = 9.8 \, \text{m/s}^2$, and $r = 100 \, \text{m}$):$$v = \sqrt{0.35 \times 9.8 \times 100} \approx 19 \, \text{m/s}$$Therefore, the car will begin to skid sideways at a speed of approximately 19 m/s.

A 1000-Kg Car Is Slowly Picking Up Speed as It