(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A road is to be banked so that any vehicle can take the bend at a speed of 30 ms^-1 without having to rely on sideways friction. The radius of the curvature of the road is 12m. At what angle should it be banked?

2. Relevant equations

various inclined slope equations...

3. The attempt at a solution

I got

[tex]N\cos\theta = mg[/tex],

[tex]N\sin\theta = \frac{mv^2}{r}[/tex],

so

[tex]\tan\theta = \frac{v^2}{gr}[/tex]

[tex]\therefore \theta = 82.4^{\circ}[/tex]

BUT, I have a question about this:

From a simple inclined slope, we have [tex]N = mg\cos\theta[/tex]

So, [tex]mg\cos\theta\sin\theta = \frac{mv^2}{r}[/tex]

But subbing in [tex]\theta = 82.4^{\circ}[/tex] now doesn't work! How come??

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# Homework Help: Banked road

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