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## Homework Statement

Problem 6.7[/B]

Radius of curve: 200m

Speed: 90 km/h=90000m/h

What should be the value of the banking angle if no dependence is to be placed on friction?

## Homework Equations

##F=ma##

##F_c=\frac {mv^2} {r}##

##w=mg##

Trig functions

## The Attempt at a Solution

I got an answer that is flipped from the book’s key. My work is below:

N=normal force

##N=F_c * sin \theta = \frac {mv^2} {r}* sin \theta ##

##N=w*cos \theta=mg*cos\theta##

##\frac {mv^2} {r}* sin \theta = mg*cos\theta##

##\frac {sin \theta} {cos\theta} =tan \theta= \frac {gr} {v^2}##

However, the key says that ##tan\theta= \frac {v^2} {gr}## For example I’m particularly not sure how they set up the equation ##w= N cos \theta## .I thought it should be ## N= w cos\theta##? I tried to draw out the triangle diagram but still can't figure it out.

Thank you!