Circular Motion Question (Possibly Easy?)

[BlakeGriffin]

Homework Statement

A highway curve of radius 420m is designed for traffic moving at a speed of 73.0 km/hr .

What is the correct banking angle of the road?

Homework Equations

V=(2(pi)(r)/T)
a=(v^2)/r

The Attempt at a Solution

I feel like this is an easy question but for some reason I can't get it.

r=420m
v=73 mi/hr which is 20.3 m/s

I was going to use a free body diagram to find the normal force then use the cos and sin stuff to find the angle but since the mass is not given I don't know what to do.

I don't know where to go exactly? Can anyone just tell me what I'm missing here?

 

[Oldblood]

A body that moves in a circle needs a net force to move in this circle. If the circle has a radius R and the body moves with a speed v then the force needed to keep the body in the circle is given by mv^2/r, using Newtons first law and sentriple aceleration. This is one way to write this force

F=mv^2/r

So, what force is it that keeps it in the circle? Well there is no friction, so we need an angle and a component from the normal force. Do you know how to find this component? Find the component in therms og m, g and the angle and sustitute for F. Notice that the m-s cancel, so you don't need them. Then solve for the angle and youre done.

 

[cepheid]

Basically, for a flat road, friction is what provides the centripetal force that keeps the car moving in a circle. If you bank the curve, then there is also a component of the weight that is parallel to the incline that helps you out as well. Draw the free body diagram and set up the equations, and you should see that mass doesn't matter (it cancels from both sides of the equation).

 

[Oldblood]

Btw, your first equation is not relevant

 

[BlakeGriffin]

So is this what the free body diagram looks like then?

http://img851.imageshack.us/img851/3382/232.jpg

Dash marked lines are the components of normal force.

 

[cepheid]

I was having trouble interpreting that FBD, but if the vertical force is weight and the oblique one is the normal force, then that looks right. So, is there no friction in this problem? If not, then the FBD is complete.