Banking Angle Calculation for Highway Curve with Given Velocity and Radius

[daniellelok]

Homework Statement

the question is to find the angle that should be banked on a highway curve. the velocity is given, which is 100km/hr and the radius is 300m

Homework Equations

The Attempt at a Solution

i know i need to convert the units first, but then i don't know what to do... to find the angle, i need to use tangent to find it, or is it?? if yes, i don't know how...
please help...tmr is the physics final...thx a lot~~XDXD

 

[Mindscrape]

I can't remember if you end up getting a tangent or not, though you will probably end up with tan or cot. If you draw a careful freebody diagram, and use Newton's 2nd law properly then you can get through this problem.

 

[daniellelok]

the equation i got is that $$\tan\theta=\frac{v^2}{rg}$$. i don't know how i got this equation, but it did give me a right answer. can u help explain it?

 

[mace2]

I think you end up with mgsin0 = mv^2/r
0 = theta

if you draw a freebody diagram you should see that it is that component which creates circular motion. if I'm wrong i apologize but I'm 85% sure. :P

 

[daniellelok]

no...it should be tan, coz i got the right answer from my equation. i just don't understand how i can get the equation on #3

 

[mace2]

i think it depends on where you're counting the angle from.

draw a freebody diagram of the vehicle on the banked turn, the perpendicular component to the car's motion is the Fc. you can write it in terms of Fg and an angle.

 

[cristo]

Where did you get the equation in post 3 from then? What concepts should you use for this question? From these concepts can you attempt to derive the equation?