Final answer:
The student's question deals with understanding the forces on a train passenger when the train is traveling on a curved banked track at various speeds and tilts, and how to calculate the side force, angle of tilt needed to avoid side force, and the speed for ideal conditions without side force.
Step-by-step explanation:
The question is centered around the concept of circular motion, specifically the forces experienced by a passenger on a train moving through a curved banked track. When a train travels at a speed different from the rated speed for which the banked curve was designed, one can calculate the side force felt by a passenger using principles of physics such as centripetal force and the forces in a non-inertial frame of reference (centrifugal force from a passenger's perspective).
For the calculation involving a banked curve at an angle, the forces involved are the normal force from the track and the weight of the passenger. The banked angle and the speed of the train determine whether the passenger will feel a side force and if so, how much. To find the angle of tilt required to avoid this side force, we can use trigonometry and centripetal force equations to find the right balance.
If the train is banked too much or too little for a given speed, additional frictional force (or the absence of it) would be needed to avoid slipping. These types of problems involve a good understanding of Newton's laws of motion, centripetal force, and the concept of the fictitious centrifugal force that is observed in rotating reference frames.