# Banked Curve Problem: Find Radius with Friction Coefficients

• M1ZeN
In summary, the problem involves a car approaching a banked curve at a minimum speed of 20 m/s, with a mass of 1000 kg. The coefficients of kinetic and static friction are given as 0.5 and 1.0 respectively. Two approaches to solving the problem are suggested, one using centripetal force and the other using centrifugal force. The latter is preferred and involves sketching the situation and writing expressions for the components of each force. The minimum and maximum speeds are discussed in relation to the forces, and it is noted that kinetic friction only comes into play when the car starts to slip. The kinetic friction is less than the static friction, meaning that once the car starts to slip, it will continue
M1ZeN

## Homework Statement

A car approaches a curve that is banked at 20 degrees. The minimum speed for the curve is 20 m/s. The car's mass is 1000 kg. What is the radius of the curve if the coefficient of kinetic friction is 0.5 and the coefficient of static friction is 1.0?

## Homework Equations

I really don't know how to set up an equation for this problem. I understand that there are three forces acting upon the car, static friction, kinetic friction and force of gravity.

## The Attempt at a Solution

I understand that the coefficients both are interpreted to be:

(vector)fk = u(k)N
(vector)fs = u(s)N
(vector)Fg = mg

There are a couple of ways of looking at a banked curve problem, one using centripetal force and one using centrifugal force. I prefer the latter. Sketch your car on the slope and show the centrifugal force horizontally and outward. Gravity downward. Write expressions for the components of each that are parallel to the slope and straight into the slope. Then you can calculate the friction force.

Delphi51 said:
There are a couple of ways of looking at a banked curve problem, one using centripetal force and one using centrifugal force. I prefer the latter. Sketch your car on the slope and show the centrifugal force horizontally and outward. Gravity downward. Write expressions for the components of each that are parallel to the slope and straight into the slope. Then you can calculate the friction force.

I graphed everything out and fully understand where all the friction forces are. I'm still confused on how to interpret the coefficients in with a working mathematical equation.

At the "minimum speed" the parallel component of centrifugal force + friction just prevent the parallel gravity component from making the car slide down the slope.
At the "maximum speed" gravity + friction just prevent the centrifugal force from making the car slide up the slope.

The kinetic friction only comes into play when the car starts to slip. And it is less than the static friction so once it starts to slip, it will slip right off the road.

## What is a banked curve?

A banked curve is a curved section of road or track that is designed to allow vehicles to safely navigate turns at higher speeds. It is typically higher on the outer edge and lower on the inner edge to provide a natural inclination for the vehicle to follow.

## How do friction coefficients affect the radius of a banked curve?

The friction coefficients determine the maximum safe speed at which a vehicle can travel around a banked curve without slipping or sliding off the track. A higher friction coefficient allows for a tighter radius, while a lower friction coefficient requires a wider radius.

## What is the equation for finding the radius of a banked curve with given friction coefficients?

The equation is: R = (v^2/g)*(1+μtanθ)/(1-μ), where R is the radius, v is the speed, g is the acceleration due to gravity, μ is the coefficient of friction, and θ is the angle of the banked curve.

## Can the radius of a banked curve be calculated without knowing the friction coefficients?

No, the friction coefficients are necessary in order to determine the radius of a banked curve. Without this information, it is impossible to accurately calculate the maximum safe speed for the curve.

## What factors can affect the friction coefficients in a banked curve?

The friction coefficients can be affected by various factors such as the type of surface material, weather conditions, and the weight and type of vehicle traveling on the curve.

• Introductory Physics Homework Help
Replies
18
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
978
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
2K