# Uniform circular motion - centripetal force and banked curves

1. Jun 4, 2005

### dippedindettol

well first off, here's the problem:

A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.997. At what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction?

now i honestly don't know how to go about doing this. i can't get the speed or even the force Fc, because the only cvariable given is the coefficient of static friction; no mass, no radius of curve, nothing.

is this one of those weird concept problems? can anyone guide me towards solving this?

thx alo

2. Jun 4, 2005

### whozum

You'd have better luck in the homework help section.

The trick to the banked curve problems is to realize that the force of friction and a certain component of the normal force add up to the centripetal force. The best way to see this is to start with a force diagram, and note that the vertical forces add up to zero.

Obviously since there are no numbers given, it is a conceptual problem. It wants you to compare the turning angle and speed with a banked curve as opposed to an unbanked curve. The banked curve I already described above, and for the unbanked curve, the friction force is the only contributor to the centripetal motion.

3. Jun 5, 2005

### Staff: Mentor

This is not a conceptual problem; you are given all the data you need to find the angle. (Since the max speed and the radius of the curve remain the same, they will drop out of the final result.)

Start by analyzing the unbanked curve. Apply Newton's 2nd law.

Then analyze the banked curve. Apply Newton's 2nd law for both horizontal and vertical directions.

You'll then combine all three equations to solve for the angle.

Hint: Does the centripetal acceleration change for the banked road case?

4. Jun 5, 2005

### F|234K

i once asked a question very similar to this (and it's solved). look at the posts i made to find that problem.

it might help a bit...

Last edited: Jun 5, 2005