- #1
AznBoi
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Homework Statement
An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. She does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the circular path.
a) Show that for a given speed (v) and a radius (r), the curve must be banked at the angle (theta) such that [tex]tan \theta= \frac{v^2}{rg}[/tex]
b) Find the angle at which the curve should be banked if a typical car rounds it at a 50m radius and a speed of 13.4 m/s.
Homework Equations
[tex]tan \theta= \frac{v^2}{rg}[/tex]
The Attempt at a Solution
I have no idea what a) means or how to start it. I know that you have to show it by using the variables given. However, I don't know how you would show it. =P
b) [tex]tan \theta= \frac{v^2}{rg}[/tex]
[tex]tan \theta= \frac{13.4m/s^2}{(50m)(9.8m/s^2)}[/tex]
[tex] tan \theta= 0.366449 radians [/tex]
[tex] \theta= tan^{-1}{}0.366449 radians [/tex]
theta=20.125 radians
Thanks for your help!