Centripetal Force - Banked Curve

[Nicolaus]

Homework Statement

A 1000kg car travels around a frictionless banked curve having a radius of 80m. If the banking is 20 degrees to the horizontal, at which specific speed must the car travel to maintain a constant radius?

Homework Equations

Fc = mv^2/r
Fg(perp.) = mgcos(20)

The Attempt at a Solution

Would someone explain to me why we use the perp instead of the parallel angle on the incline? Is it because the car is traveling in the straight (toward the plane) direction along the banked curve?

 

[voko]

What do you mean by "parallel" and "perpendicular" angles?

 

[Nicolaus]

I meant the force of gravity parallel and perp to the incline.

 

[voko]

In the parallel and perpendicular coordinate axes, what is the reaction force and what is the acceleration?

 

[lep11]

Here's a diagram I made. N_x=m*v^2/r and N_y-G=0
we get two equations
N*sin20=mv^2/r and
N*cos20=mg
Then solve for v.

 

[Nicolaus]

Thank you.