An engineer is designing a banked circular curve of radius 25 m in a new bicycle velodrome.
Diagram A shows the bicycle approaching the banked section, and diagram B shows the front view of a bicycle moving out of the page as it rounds the banked bend.
The bicycle is travelling at 11 m s\(^{-1}\) on the banked section. At this speed there are no sideways frictional forces between the wheels and the road surface.
Determine the angle of the banked bend with the road surface, giving your answer to the nearest degree. (3 marks)
Show Worked Solution
| \(\tan \theta\) | \(=\dfrac{F_c}{mg}\) | |
| \(F_c\) | \(=mg \tan \theta\) | |
| \(\dfrac{mv^2}{r}\) | \(=mg \tan \theta\) | |
| \(\dfrac{v^2}{r}\) | \(=g \tan \theta\) | |
| \(\tan \theta\) | \(=\dfrac{v^2}{gr}\) | |
| \(=\dfrac{11^2}{9.8 \times 25}\) | ||
| \(\theta\) | \(=\tan^{-1}\Big(\dfrac{11^2}{9.8 \times 25}\Big)\) | |
| \(=26^{\circ}\) |