Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20 m/s can safely negotiate the curve if the radius of the curve is 200m.

Question

Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20 m/s can safely negotiate the curve if the radius of the curve is 200m. 
* Data: 
v=20 m/s 
r=200m 
*Formula 
TAN(theta)=v^2/rg 
*Solution 
TAN(theta)=(20 m/s)^2/(200m)(9.8 m/s^2) 
TAN(theta)=(400 m^2/s^2)/(1960 m^2/s^2) 
TAN(theta)=.204 Degrees 
Thank You For Your Time! JL

Damon · Accepted Answer

N is normal force from road

m g = N cos T
so N = m g/cos T

N has inward component = N sin T
so inward component of force
= m g sin T/cosT = m g tan T

Ac = m v^2/R
m g tan T = m v^2/R
tan T = v^2/( Rg) as you know
tan T = 400/(200*9.81)
tan T = .204
T = 11.5 degrees

Jose Luis · Answer

Nice! Thanks Again Damon, you're the best. The Master will point the way; however, I must make the effort. Thank you so much for pointing the way. Many Blessings!

n · Answer

Correct answer..I got the same