Part A
A good roller coaster wreaks havoc with the riders apparent weight. Calculate the magnitude of the force exerted by their seat on a rider with a (regular) weight of 700 N at the points labeled A-F in the picture below, assuming the coaster starts from rest at the top of the first hill and that the coaster is frictionless. (Recall that this seat force will give an idea of how "heavy" the rider feels at each point in the ride.) For Part A, use the values:
h1 |
h2 |
h3 |
r1 |
r2 |
r3 |
|---|
System: Rider as point particle.
Interactions: The conservative influence from the earth (gravity) will be assigned a potential energy for this problem. The seat's influence (normal force) is the only non-conservative force, but since the rider travels with velocity always parallel to the track, the normal force is always perpendicular to the path and does zero work, and so we will neglect it when using the Mechanical Energy and Non-Conservative Work model. The normal force will be relevant for the dynamics of the car.
Models: Uniform Circular Motion, Point Particle Dynamics and Mechanical Energy and Non-Conservative Work.
Approach: We begin by using Point Particle Dynamics to relate the normal force from the seat to other quantities. This requires free body diagrams: