**You are asked to build a country fair version of an old classic motocycle stunt in which the riders start inside a circular enclosure with vertical walls about 4.90 meters high. Around the top of this enclosure is a circular platform around which the patrons stand to witness the spectacle. At the bottom of the walls there is a narrow ramp about 0.70 meter wide, inclined at 45 degrees to the horizontal and running around the base of the walls.
The motorcyclists, usually 3 for maximum effect, start by riding in a circle on the grass in the interior of the enclosure and gradually increase their speed and the radius of their circles until they reach the inclined ramp. Riding along this inclined ramp they further increase their speed while maneuvering up onto the vertical wall. They then increase their speed even further until they are rocketing around the enclosure seemingly oblivious to the fact that they are riding with their motorcycles practically horizontal.
Assuming that, for safety, the motorcyclists must not be asked to travel at more than 75.0 km/hr and that, also for safety, their acceleration should not be more than 3.40 g’s (g is the acceleration due to gravity:9.80 m/s^2), what diameter, in meters, should you make the enclosure so that they can indeed travel at this maximum speed?**
I don’t even know where to start with this question.
All I’ve done is draw what the enclosure looks like, a free-body diagram for the circular motion in the grass area of the enclosure, a free-body diagram for the circular motion on the ramp, and a free-body diagram of the circular motion along the vertical walls.
Since the speed in increasing (to ultimately reach 75 km/h= 20.8 m/s), this isn’t uniform circular motion.
The forces in the grassy area are the gravitational force (downward), the normal force (upward), and the static friction force. Since the speed is nonuniform, the force doesn’t point towards the center of the circular path and can be resolved into Fr (towards center) and Ftan (parallel to velocity vector).
The forces on the ramp are the same but the normal force is perpendicular to the ramp’s slope and can be resolved into its components (Fny=Fncos45) and Fnx=Fnsin45).
The forces against the vertical wall are the normal force exerted by the wall to the motorcycle, the gravitational force pointing downward, and the frictional force pointing upward.
I am not sure where to start to get the answer they are looking for and would appreciate some guidance. Thanks for reading!