# A banked curve and coefficient of friction

• praecox
In summary, the problem involves finding the minimum coefficient of friction for a banked circular highway curve designed for traffic moving at 56 km/h, with a radius of 203 m. On a rainy day, the traffic is moving at 51 km/h. Using the equations tan x = v^2/(gr) and a = v^2/r with the given values, the minimum coefficient of friction is found to be approximately 0.021. The issue with the solution may be due to rounding errors, so it is recommended to keep all digits in intermediate calculations and round only the final result.
praecox

## Homework Statement

A banked circular highway curve is designed for traffic moving at 56 km/h. The radius of the curve is 203 m. Traffic is moving along the highway at 51 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road?

## Homework Equations

tan x = v^2/(gr) with the v(designed)

a = v^2/r with the v(rainy)

coef of friction = (gsin(x) - acos(x))/(gcos(x)+asin(x))

## The Attempt at a Solution

I have these values for my variables:
v(designed) = 15.6 m/s
v(rainy) = 14.2 m/s
x (the angle of the bank) = 6.97°
a = 14.17^2/203 = 0.989

so, coef of friction should be:
[9.8sin(6.97) - .989cos(6.97)] / [9.8sin(6.97) + 9.8cos(6.97)]
= 0.2075/9.84759
= 0.021

I used the exact same equation on my homework for three practice problems and they all came out right. I've tried 4 different variations of this with different decimal points or rounding the angle to 7° or acceleration to 1, but it still says it's wrong! grrrr...

I only get one more submission before I can't try anymore. Can someone please check my math on this? Thanks so much!

I think it's just rounding error. Try keeping all the digits on intermediate calculations and rounding only the final result.

## 1. What is a banked curve?

A banked curve is a curved section of a road or track that is angled or tilted towards the inside of the curve. This allows vehicles to safely navigate the curve at higher speeds without sliding off the road or track.

## 2. How does a banked curve affect a vehicle's path?

A banked curve helps to counteract the centrifugal force that pulls a vehicle outwards when turning. This allows the vehicle to follow a curved path without sliding off the road or track.

## 3. What is the relationship between banked curve angle and speed?

The angle of a banked curve is directly related to the speed at which a vehicle can safely travel through it. Higher speeds require a steeper banked angle to counteract the centrifugal force.

## 4. What role does coefficient of friction play in a banked curve?

The coefficient of friction is a measure of the grip or traction between two surfaces. In a banked curve, a higher coefficient of friction between the tires and the road or track surface allows for better control and stability while turning.

## 5. How is the coefficient of friction calculated for a banked curve?

The coefficient of friction for a banked curve can be calculated by dividing the horizontal component of the centrifugal force by the vertical component of the weight of the vehicle. This value is also affected by factors such as the angle of the banked curve and the type of surface material.

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