Question

On an icy day, the coefficient of friction between a car's tires and the expressway exit ramp is 0.171. The radius of the exit curve is 88.9 meters. The exit ramp is completely level. Determine the maximum speed with which the car can move through the ramp without sliding.

Answer 1

Apply Newton’s Second Law in the direction towards the radius of the curve.

`F = ma_(rad) = (mv^2)/(R)\\F = F_(friction)\\F_(friction) = (mv^2)/(R)`

`\mu mg = (mv^2)/(R)\\v = √(\mu Rg) = √(0.171* 9.8 * 88.9) = 148.97~m/s`

Explanation:

On the exit curve, the car is making circular motion. The only force that balances its centripetal force is the force of friction. Otherwise, the car would slide off the road.