Circular motion: bicycle moving in a circle. Find speed given r and degree

[s1gma]

Homework Statement

A bicycle is racing around on a horizontal surface in a circle of radius 19 m. The force exerted by the road on the bicycle makes an angle of 23 degrees with the vertical. What is its speed?

Homework Equations

I believe this is a uniform circular motion problem, so I've been trying these equations:

$$\Sigma$$ F = ma


a = $$\frac{v^{2}}{r}$$

Where v is the tangential velocity (what I need to find) and a is the acceleration pointing inward causing it to turn, r is the radius.

The Attempt at a Solution

I thought this problem was a mistake at first because I'm given an angle and a radius, and I'm somehow supposed to derive a speed. I broke down the angle into component vectors where x = 0.39 and y = 0.92. I know that the x component points inward to the center of the circle and should be the radial component for a circular motion problem. I could use that as a then just plug in r and solve for v.

However, I don't know the real magnitude of the force from the earth, so I don't know how to find a. This is the only way to solve it that I can think of. Can someone guide me here?

 

[s1gma]

Got it! After looking it over for a while I started from the beginning, this time setting up the y equation so we have:

Fnet x = n*sin(theta) = (mv^2) / (r)
Fnet y = n*cos(theta) - mg = 0

You can solve the y equation for n and then plug it into the n of the x equation so that the mass cancels out and you eventually end up with just the radius, g, and tangent of the angle theta which are all known. Solution was 8.89 m/s.

Thanks anyway.