What Is the Correct Banked Curve Angle for a Car Traveling at 64 km/hr?

[Maiia]

Homework Statement

A curve of radius r is banked at angle θ so that a car traveling with uniform speed v can
round the curve without relying on friction to keep it from slipping to its left or right.
The acceleration of gravity is 9.8 m/s2. If r = 50 m and v = 64 km/hr, what is θ?
Answer in units of ◦.

For this one, I drew a FBD. In my picture, Fny and Fg canceled each out, so the unbalanced force was Fnx. I used N2nd Fnet=ma and used components:
Fnx=max
Fnsintheta=max
Fny= mg
Fncostheta=mg
then i divided them:
Fsintheta max
--------- = --------
Fcostheta mg
The masses canceled out on the right and on the left I had tantheta.
on the right, ax/g= v^2/rg
When I plugged in numbers, I got theta= approx 90 degrees. However, when I submit this answer, it is wrong..could someone help me find out where I messed up?

 

[jgens]

It's hard to follow your work but it looks like your resultant equation is correct: tan(x) = v^2/rg. Make sure to convert the km/hr to m/s before doing the calculation.

 

[LowlyPion]

Homework Statement

A curve of radius r is banked at angle θ so that a car traveling with uniform speed v can
round the curve without relying on friction to keep it from slipping to its left or right.
The acceleration of gravity is 9.8 m/s2. If r = 50 m and v = 64 km/hr, what is θ?
Answer in units of ◦.

For this one, I drew a FBD. In my picture, Fny and Fg canceled each out, so the unbalanced force was Fnx. I used N2nd Fnet=ma and used components:
Fnx=max
Fnsintheta=max
Fny= mg
Fncostheta=mg
then i divided them:
Fsintheta max
--------- = --------
Fcostheta mg
The masses canceled out on the right and on the left I had tantheta.
on the right, ax/g= v^2/rg
When I plugged in numbers, I got theta= approx 90 degrees. However, when I submit this answer, it is wrong..could someone help me find out where I messed up?

The force down the bank will be m*g*sinθ and the force from centrifugal acceleration is your m*v²*cosθ/r

That means that you have v²/(r*g) = tanθ

So to find θ that would be the tan^-1( v²/(r*g)) = θ

 

[Maiia]

oh that would be the problem, not converting the units >< thanks to both of you for your help! :)