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 (for which no friction is needed to stay on the run) for the smaller radius curve is v . What is the safe speed on the larger-radius curve?
A) $v / 2$
B) $v \sqrt { 2 }$
C) $v / \sqrt { 2 }$
D) $2 v$

Question

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 (for which no friction is needed to stay on the run) for the smaller radius curve is  v . What is the safe speed on the larger-radius curve?
A) $v / 2$
B) $v \sqrt { 2 }$
C) $v / \sqrt { 2 }$
D) $2 v$

Quizplus · Accepted Answer

The safe speed on a banked curve depends on the radius of the curve and the banking angle. For a given angle, the safe speed is proportional to the square root of the radius. If one curve has twice the radius of the other, the safe speed for the larger-radius curve is $v \sqrt{2}$, because the square root of 2 times the radius results in a safe speed that is the square root of 2 times the original speed.

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