example1: level curves\nconsider a car driving at 20 m/s (~45 mph) on a level circular turn of radius 40.0…

Explanation:

Step1: Identify centripetal - force formula

The centripetal force $F_c$ acting on the car is provided by the frictional force $F_f$. The centripetal - force formula is $F_c=\frac{mv^{2}}{r}$, where $m$ is the mass of the car, $v$ is the speed of the car, and $r$ is the radius of the circular path.

Step2: Calculate the frictional force

Given $m = 1000\ kg$, $v=20\ m/s$, and $r = 40.0\ m$. Substitute these values into the centripetal - force formula: $F_f=F_c=\frac{mv^{2}}{r}=\frac{1000\times20^{2}}{40}=10000\ N$.

Step3: Relate frictional force to coefficient of friction

The frictional force is given by $F_f=\mu N$, where $N$ is the normal force. On a level road, $N = mg$ (where $g = 9.8\ m/s^{2}$). We know $F_f=\mu mg$, and we want to find $\mu$. Rearranging for $\mu$ gives $\mu=\frac{F_f}{mg}$.

Step4: Calculate the coefficient of friction

Substitute $F_f = 10000\ N$, $m = 1000\ kg$, and $g=9.8\ m/s^{2}$ into the formula for $\mu$: $\mu=\frac{10000}{1000\times9.8}\approx1.02$.

Answer:

1. The magnitude of the frictional force is $10000\ N$.
2. The minimum coefficient of friction is approximately $1.02$.