Question

If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). what is theminimum speed required to take 84 meter radius banked at 17 degree so that you don't slide inward.

Answer 1

For the car to stay on the road without sliding in or sliding out, all the forces on the x-axis must equal each other. Thus by equating all the forces on the x-axis, we can find the coefficient of the friction.

In order to determine the minimum speed of the car, use the following expression:

`v=\sqrt[]{R\cdot g\cdot\tan \theta}`

where,

R: radius of the road = 84m

g: gravtitational acceleration constant = 9.8m/s^2

θ: angle of banking of the road = 17 degrees

Replace the previous values of the parameters into the formula for v:

`\begin{gathered} v=\sqrt[]{(84m)(9.8(m)/(s^2))(\tan 17)} \\ v\approx15.86(m)/(s) \end{gathered}`

Hence, the minimum speed requierd is approximately 15.86m/s

In order to determine the value of the minimum coefficient friction required, use the following formula:

`\mu=(v^2-Rg\tan \theta)/(v^2\tan \theta+Rg)`

by replacing, you get: