- #1
logan3
- 83
- 2
Homework Statement
A highway curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve
is effectively frictionless. What is the speed with which to take the curve without tending to
slide either up or down the surface of the road?
[itex]r = 80m[/itex]
[itex]\theta = 45^o[/itex]
[itex]g = 9.8m/s^2[/itex]
Homework Equations
[itex]F_c = F_N sin \theta = mv^2/r[/itex]
[itex]F_N = mgcos \theta[/itex]
The Attempt at a Solution
[itex]F_N sin \theta = \frac {mv^2}{r} \Rightarrow (mg cos \theta)sin \theta = \frac {mv^2}{r} \Rightarrow v = \sqrt{rg cos \theta sin \theta}[/itex]
[itex]\Rightarrow \sqrt{(80m)(9.8m/s^2)cos 45^o sin 45^o} = \sqrt{392m^2/s^2} = 19.8m/s [/itex]
I know the answer's supposed to be 28m/s and I'm missing a tangent somewhere to make it [itex]v = \sqrt{rgtan \theta}[/itex] instead, but I can't figure out where.
Thank-you