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 is given by the formula:

v = $\sqrt { r g tan\theta }$

Where r is the radius of the curve, g is the acceleration due to gravity and $\theta$ is the angle of banking.

Since both curves are banked at the same angle, but one has twice the radius of the other, the safe speed on the larger radius curve can be found by substituting 2r for r in the above equation:

v' = $\sqrt { 2r g tan\theta }$

v' = $\sqrt { 2(r g tan\theta) }$

v' = $\sqrt { 2(v^2) }$  (since v = $\sqrt { r g tan\theta }$ for the smaller radius curve)

v' = v $\sqrt { 2 }$

Therefore, the safe speed on the larger radius curve is v times the square root of 2, or choice C: v $\sqrt { 2 }$.

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