Question

Two banked curves have the same radius. Curve A is banked at an angle of 11.2°, and curve B is banked at an angle of 21.2°. A car can travel around curve A without relying on friction at a speed of 19.0 m/s. At what speed can this car travel around curve B without relying on friction? Two banked curves have the same radius. Curve A is banked at an angle of 11.2°, and curve B is banked at an angle of 21.2°. A car can travel around curve A without relying on friction at a speed of 19.0 m/s. At what speed can this car travel around curve B without relying on friction? @Physics

Answer 1

If a curve is banked, there is a gravitational force pulling down the incline equal to
\[mg\sin(\theta)\]
Furthermore, if you consider only the component pulling down the incline, the centripetal force required to keep the object moving in a circular path is
\[F = \frac{mv^2cos(\theta)}{r} \]
therefore,
\[mgsin(\theta) = \frac{mv^2cos(\theta)}{r} \]
and so
\[r = \frac{v^2\cot(\theta)}{g} \]
if the two radii are equal, that implies that
\[v_1^2\cot(\theta_1) = v_2^2\cot(\theta_2) \]
and so
\[v_2 = v_1 \sqrt{\frac{\cot(\theta_1)}{\cot(\theta_2)}} \]

Answer 2

if i wanna solve it on my calulator, i will i put cot11.2?

Answer 3

thanks i have solved it using ur solution