Finding angle to reduce friction

[maff is tuff]

Homework Statement

A car is traveling around a curve that has a radius of 500 ft. at a speed of 60mph. To what angle must the curve be banked so that there is no frictional force?

Homework Equations

The Attempt at a Solution

I have attached mt solution below. I don't know the right answer to this question but I gave it a shot. The answer I got doesn't seem weird or anything so it has a a chance of being right. I don't think I understand the concept completely so I don't know if the moves or assumptions I made are valid. I kind of just wrote down the equations I know that might be relevant and used those. I know circular motion has acceleration proportional to the square of the speed and the radius so I used that equation. I am just not sure if my diagrams are correct and if I'm allowed to set equal the things that I set equal. So could you guys point out what is wrong and give me some hints on how to fix it? Or if it is right can you confirm? Thanks a lot for the help :)

 

[jaumzaum]

4 forces really act in the car. Ff, Fc, P, N.
If we have N=0, we have Ff=0
N=PcosI - FcsenI
P=Fc tanI
so mg = mV²/R tanI
tanI = gR/V²

500ft = 152,4m
60mph = 26,8224 m / s

I>60º

 

[maff is tuff]

I'm sorry you lost me. I have never seen that notation. I know N is normal force. Is Ff forward force? P parallel? And I don't know what Fc is. Why would normal force=0? Sorry I am not following.

 

[jaumzaum]

kkk
That answer I've written in brazilian notation, I'm sorry.
I'm going to translate
Ff would go for friction force, that in BR is Força de atrito
Fc would go for centripetal force that in brazil is Força centrípeta
P would go for weght that in brazil is peso
N is normal

Ff = N.u, if Ff = 0, N is null


John

 

[maff is tuff]

So could you tell me what I did wrong, like at which step I made my first error?

 

[ideasrule]

The centripetal acceleration is horizontal, not parallel to the ramp, because it points towards the center of the circle that the car traces out.

 

[maff is tuff]

So that means my force diagram is incorrect?

 

[vela]

The forces you drew were okay, but when you applied F=ma, the resulting equations were wrong because the centripetal acceleration has components in both the x and y directions for your choice of axes.

 

[maff is tuff]

Ok thanks guys I'll work on the problem when I get home and I'll let you know if I have any more problems. Thanks again.