QuestionHW9.5. Frictional Force between Tires and the Road
A racecar of mass $m$ is driving around a horizontal circular track of radius $R$ at constant speed $v$ . The frictional force between the tires of the racecar and the road is at its maximum value.
Write the expression to find the value of the coefficient of friction between the tires and the road in terms of the mass $m$ , velocity $v$ , radius $R$ , and the acceleration of free-fall $g$ .
Note that it may not be necessary to use every variable. Use the following table as a reference for each variable: For Use m m $v \mathrm{v}$ $R$ R $g \quad \mathrm{~g}$

Studdy Solution
Solve for the coefficient of friction.
Since the car is on a horizontal track, the normal force $N$ is equal to the gravitational force: $N = mg$
Substitute $N = mg$ into the frictional force equation: $\mu mg = \frac{mv^2}{R}$
Cancel out the mass $m$ from both sides: $\mu g = \frac{v^2}{R}$
Solve for $\mu$ : $\mu = \frac{v^2}{gR}$
The expression for the coefficient of friction is: $\mu = \frac{v^2}{gR}$

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