Circular motion problem no idea what's going wrong ><

[irNewton]

Homework Statement

A highway curve of radius 560m is designed for traffic moving at a speed of 73.0km/hr (1216m/s). What is the correct banking angle of the road?

Homework Equations

a=v^2/r
F=ma

The Attempt at a Solution

Forces in t direction:
Fnet=Fncos$$\vartheta$$-Fg=0
Fn=mg/cos$$\vartheta$$=0


Forces in r direciton:

Fnetr=Fnsin$$\vartheta$$=mv^2/r
mgsin$$\vartheta$$/cos$$\vartheta$$=mv^2/r
tan$$\vartheta$$=v^2/r*g
$$\vartheta$$=tan-1(1216^2/(9.81*560))
$$\vartheta$$= 90 degrees?

which is wrong... = (

 

[gamer_x_]

double check the way you're assigning your forces, is the Fny component which is cancelling vertical gravity the hypotenuse of the triangle? I find it helpful in these cases to rotate the coordinate system so that the x-axis is actually the sloped road. That way your Fn has only 1 component, and you break down gravity into y & x where x points towards the center of the turn.