What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?
A)$51 ^ { \circ }$
B) $61 ^ { \circ }$
C) $31 ^ { \circ }$
D) $41 ^ { \circ }$

Question

What is the proper banking angle for an Olympic bobsled to negotiate a  100-m radius turn at 35  m/s without skidding?
A)$51 ^ { \circ }$
B) $61 ^ { \circ }$
C) $31 ^ { \circ }$
D) $41 ^ { \circ }$

Quizplus · Accepted Answer

The proper banking angle ($\theta$) for a bobsled (or any vehicle) to negotiate a turn without skidding can be found using the formula for the centripetal force required for circular motion, which is provided by the gravitational force component acting down the slope of the bank. This is given by $\tan(\theta) = \frac{v^2}{rg}$, where $v$ is the velocity, $r$ is the radius of the turn, and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Plugging in the given values ($v = 35 m/s$, $r = 100 m$), we get $\tan(\theta) = \frac{(35)^2}{100 \times 9.8}$, which simplifies to $\tan(\theta) \approx 1.225$. Solving for $\theta$ gives $\theta \approx 51^\circ$.

What Is the Proper Banking Angle for an Olympic Bobsled 51∘51 ^ { \circ }51∘

What Is the Proper Banking Angle for an Olympic Bobsled $51 ^ { \circ }$