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 /
B)2v
C)v
D)v/2

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 / 
B)2v 
C)v 
D)v/2

Quizplus · Accepted Answer

The safe speed on a banked turn can be given by the formula: 
v=sqrt(rgtanθ)
where r is the radius of the turn, θ is the angle of banking, and g is the acceleration due to gravity.

Given that the angles of banking are the same, and one radius is twice the other, we can take the ratio of the two speeds:

v_larger = sqrt((2r_smaller)tanθ) 
= sqrt(2rtanθ) * sqrt(r_smaller tanθ) 
= sqrt(2) * v_smaller

Therefore, the safe speed for the larger curve is  v_larger = sqrt(2) * v_smaller = v * sqrt(2).

So, the correct answer is option C.

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