What Range of Speeds Allows a Car to Safely Navigate a Wet, Banked Curve?

[botab]

Hello PF, I need some assistance with this problem.

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.]

how should I start this question @_@

 

[Kurdt]

Hello botab. Units would help anyone looking at this question. numbers are meaningless if they don't have any units to tell you what they are measuring.

Basically you're going to need to consider the circular motion of the car. When the car travels in a circle there is a centrifugal force which is opposed by the friction betwen the road and the tyres. At some speed the centrifugal force will be too great for the friction to cope with and the car will spin out.

 

[nlightner]

To solve this problem, we need to consider the forces acting on the car as it goes around the curved road. The two main forces at play are the centripetal force, which keeps the car moving in a circular path, and the friction force, which prevents the car from slipping off the road.

First, we can calculate the centripetal force using the formula Fc = mv^2/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve. In this case, we know the radius (61) and the design speed (89), so we can plug those values in to find the required centripetal force.

Next, we need to consider the direction of the friction force. When the car is going too slow, the friction force will act in the same direction as the centripetal force, helping to keep the car on the road. However, when the car is going too fast, the friction force will act in the opposite direction, trying to push the car off the road.

To calculate the maximum safe speed, we need to find the point where the friction force is equal to the coefficient of static friction (0.32) multiplied by the normal force (which is equal to the car's weight). This will give us the maximum speed at which the friction force can counteract the centrifugal force and keep the car on the road.

Using these calculations, we can determine the range of speeds at which the car can safely make the curve. Any speed below the maximum safe speed will result in the car successfully navigating the curve, while any speed above the maximum safe speed will result in the car slipping off the road. I hope this helps you get started on solving the problem.