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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?

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# Homework Help: Banked curve problem

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