Question

A car racing on a flat track travels at 22 m/s around a curve with a 56-m radius. Find the car’s centripetal acceleration. What minimum coefficient of static friction between the tires and road is necessary for the car to round the curve without slipping?

Answer 1

Answer:

0.88

Explanation:

velocity (v) = 22 m/s

radius (r) = 56 m

acceleration due to gravity (g) = 9.8 m/s^{2}

What minimum coefficient of static friction between the tires and road is necessary for the car to round the curve without slipping?

for the car to successfully go round the curve, the frictional force must be equal to or greater than the normal force, therefore

Normal force = frictional force

ma = μmg

where

• m = mass of the car

• μ = coefficient of friction
• g = acceleration due to gravity

• a = $\frac{v^{2} }{r}$ = $\frac{22^{2} }{56}$ = 8.6
• putting in all required values the equation now becomes

        8.6m = μm x 9.8

        8.6 = 9.8 x  μ

          μ = 8.6/9.8 = 0.88