Rotational Motion of a car on a curve

[ajmCane22]

Homework Statement

A 600 kg car is going around a banked curve with a radius of 110m at a speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

Homework Equations

N cos{theta} = mg
N sin{theta} = mv^2/r

The Attempt at a Solution

I was told to divide the second equation by the first equation which gives tan{theta} = v^2/rg
I used this equation and got the right answer, but I'm just wondering if somebody could please explain WHY the second equation was divided by the first and not the other way around.

 

[cepheid]

I was told to divide the second equation by the first equation which gives tan{theta} = v^2/rg
I used this equation and got the right answer, but I'm just wondering if somebody could please explain WHY the second equation was divided by the first and not the other way around.

If you divided the first equation by the second, you would get:

cot(θ) = (gr/v²)

θ = arccot(gr/v²).

I imagine that ought to give you the right answer as well...

 

[ajmCane22]

This might be a really dumb question, but why do you divide instead of multiply?

 

[cepheid]

This might be a really dumb question, but why do you divide instead of multiply?

You do whatever algebraic manipulation makes it easiest to solve for theta. With N's on both lefthand sides, and m's on both righthand sides, it seems natural to get rid of both of them by dividing them out. Then you're left with something that is only in terms of theta on the lefthand side.