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 (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve?

Answer 1

safe speed for the larger radius track u= √2 v

Step-by-step explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now,
`\sum F = (mv^2)/(r_1) =(mu^2)/(r_2)`................ii

form i and ii we can write

`v^2= (1)/(2) u^2`

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v