A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s.What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²) A)0.024 B)0.23 C)0.28 D)1.2

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Quizplus · Accepted Answer

The minimum coefficient of friction ($μ$) required to prevent the car from slipping can be found using the formula for centripetal force ($F_c$) required to keep the car moving in a circle, which is $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is the velocity, and $r$ is the radius of the curve. The frictional force ($F_f$) provides this centripetal force, and $F_f = μmg$, where $g$ is the acceleration due to gravity. Setting $F_c = F_f$, we get $\frac{mv^2}{r} = μmg$. Solving for $μ$ gives $μ = \frac{v^2}{rg}$. Substituting $v = 12.0 \, m/s$, $r = 52 \, m$, and $g = 9.8 \, m/s^2$, we find $μ = \frac{(12.0)^2}{52 \times 9.8} \approx 0.28$.

A 1 500-Kg Car Rounds an Unbanked Curve with a Radius