- #1

praecox

- 17

- 0

## 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!