Centripetal force?

Question

Two banked curves have the same radius. Curve A is banked at an angle of 13 degrees, and curve B is banked at an angle of 19 degrees. A car can travel around curve A without relying on friction at a speed of 18m/s. At what speed can this car travel around curve B without relying on friction.

Answer 1

((mv^2)/r)cosθ = mgsinθ
v^2 = grtanθ
(v^2)/(gtanθ) = r
v^2 = (18^2)*0.34433/0.23087
v^2 = 324*1.49145
v^2 = 483.2287
v^2 = 21.98 m/s

Answer 2

ok

so at 18 m/s, the car can go at a 13 degree bank. so the outward centripetal force is 324m/r, with m being mass of car and r being radius. a 13 deg bank means the outward force pointing out along the slope is 324m/r cos 13, or roughly 315.7m/r. so this means mgsin13=315.7m/r, which is about 2.205 m = 313.7 m/r. the m's cancel and u can solve for r, which is 143.2 meters.

so for curve b, mgsin19 = mv^2/r * cos 19

g sin 19 = v^2 cos 19 /r
v^2 = gr sin 19/cos 19
=gr tan 19
v= rt(gr tan 19)
=rt(9.8*143.2*tan19)
=21.98 m/s
or about 22 meters per second.

Answer 3

if there is no friction v=(rgtan t)^1/2

therfore v1/v2= (tan t1/tan t2)^1/2
put the values and find v2