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 / $\sqrt { 2 }$
B) 2v
C) v $\sqrt { 2 }$
D) v/2

Question

Quizplus · Accepted Answer

The safe speed on a banked curve can be calculated using the equation v=sqrt(rgtanθ), where v is the safe speed, r is the radius of the curve, g is the acceleration due to gravity, and θ is the angle of banking. Since the curves are banked at the same angle, θ is the same for both curves. Let the radius of the smaller curve be r and the radius of the larger curve be 2r. Using the equation above, the safe speed on the smaller curve is v=sqrt(rgtanθ). To find the safe speed on the larger curve, we substitute 2r for r in the same equation: v=sqrt(2rgtanθ). Simplifying this expression, we get v/√2=sqrt(rgtanθ). Therefore, the safe speed on the larger curve is v/√2.

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