Solve Banked Curve Problem: theta=21deg, Mu=0, r=150m

[N_L_]

http://img138.imageshack.us/img138/2042/untitled15mr.jpg

theta = 21 degrees
Mu = 0
radius = 150 meters
a = radial acceleration of uniform circular motion

a = v^2 / r

The sum of all forces = m*a

Since the car is at an angle and Fn is always perpendicular I split it into X and Y components.

Fn in the x direction = Fn sin theta
Fn in the y direction = Fn cos theta

X direction: Fn sin theta = m (v^2 / r)

Y direction: no acceleration so Fn cos theta - Fg = 0
Fn = (mg / cos theta)

By substitution into the equation for the x direction:

( mg / cos theta ) * sin theta = m (v^2 / r)

mg tan theta = m (v^2 / r)

cancelling m and re-arranging...

tan theta = ( v^2 / rg )

v^2 = tan 21 / (150 * 9.8)
v^2 = 564.28

v = 23.75 meters per second


Is this answer correct?

 

[Fermat]

Yes.
Your working is pefectly correct and the answer is correct.

There's just a little typo. You used a '/'-sign instead of a '*'-sign between the tan21 and the 150*9.8

 

[vaishakh]

Yes you are correct with the equations tan(theta) = v^2/rg.