Banked Curves in involving frictions

[Addie]

Banked Curves involving friction

Problem: A car is traveling in a circle of a radius of 50 meters, on the surface the coefcient of static friction between the car's tires and the road is .3. With a banking angle of 30 degrees.
(I attached a diagram)

So here's what's known:
Radius: R=50 m
Coeffcient of Static Friciton: us=.3
Bank angle theta: T=30 deg

First find: Maximum velocity.
I found this by knowing...
Sum of Fx: m(v^2/r)=NsinT+UsNcosT
Sum of Fy: NcosT-UsNsinT-mg

I find by Equation = Square root of{[rg (sinT+UsCost)]/CosT-(.3 x sinT)}
IT results in Vmax= 22.8 m/s
(here is where I found that equation)

PART 2
Find the apparent weight (hint apparent wieght = Fn)

This the part I'm struggling with.

So i use my Sum of Fx to find N ;
m(v^2/r)=NsinT+UsNcosT=
m(v^2/r)=(mgcosT)sinT+Us(mgcosT)cosT
m(v^2/r)=m[(gcosT)sinT+Us(gcosT)cosT]

then I get nowhere because I divide through by M, and I need to find M or N itself and its practically impossible with just this information...
please help if you can.. any help is apreciated..

 

[Doc Al]

First find: Maximum velocity.
I found this by knowing...
Sum of Fx: m(v^2/r)=NsinT+UsNcosT
Sum of Fy: NcosT-UsNsinT-mg

Note that Sum of Fy = 0

I find by Equation = Square root of{[rg (sinT+UsCost)]/CosT-(.3 x sinT)}
IT results in Vmax= 22.8 m/s
(here is where I found that equation)

You really should derive the results for yourself. That's the only way to learn it. (It's easy.)

PART 2
Find the apparent weight (hint apparent wieght = Fn)

This the part I'm struggling with.

You cannot find the apparent weight without knowing the mass of the car. But you can find out how the apparent weight compares to the normal weight (mg). Hint: Use your equation "Sum of Fy = 0" to solve for N.

 

[Addie]

Your right thanks!