Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is V. Therefore, the safe speed on the larger radius curve is
A) 2. V.
B) 0.71 V.
C) 0.5 V.
D) 1.4 V.
E) 0.10 V.

Question

Quizplus · Accepted Answer

The safe speed on a banked curve without relying on friction is determined by the formula $v = \sqrt{rg\tan(\theta)}$, where $r$ is the radius of the curve, $g$ is the acceleration due to gravity, and $\theta$ is the banking angle. Since the banking angle and gravity are constants for both curves, and one curve has twice the radius ($2r$) of the other, the safe speed for the larger radius curve is $\sqrt{2}$ times the safe speed of the smaller radius curve. Therefore, if the safe speed for the smaller radius curve is $V$, then for the larger radius curve it is $V\sqrt{2}$, which is approximately 1.4 times $V$.

Two Horizontal Curves on a Bobsled Run Are Banked at the Same