Calculating Safe Speed Range on a Banked Curve: Physics Question

[botab]

Hello PF, I need help with a physics question.


A curve of radius 61 is banked for a design speed of 89 .

If the coefficient of static friction is 0.32 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.]

A curve of radius 61 is banked for a design speed of 89 .

How would you find its range? I guess we could find a velocity, but it wouldn't be the the final velocity or the initial velocity?

 

[LowlyPion]

First start by drawing a force diagram of the car on the incline.

You have gravity acting down along the vertical.
You have centrifugal force acting outwardly and horizontal.

You need to resolve these forces into their components relative to the incline, perpendicular and parallel.

Then you have friction acting to retard up the incline motion when it is over 89 and down the incline motion when it is slower.