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 |
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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:
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Point A |
Point B |
Point C |
Point D |
Point E |
Point F |
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As usual, we have made a guess about the relative sizes of the normal force and gravity. The accuracy of this guess is not vital to solving the problem, only the direction of the forces matter (parallel to gravity, perpendicular to gravity, etc.). If the relative sizes do not make sense to you now, consider them again after solving Part A.
Technically, roller coaster seats can also exert forward (from the seat back) and backward (from the restraining straps or bars) forces on the rider. In the limit of a very short coaster (say one car) with very little friction/air resistance these forces are basically zero because gravity will accelerate the person and the coaster at the same rates. What would the seat force on a rider in the front or back car of a very long (many cars) roller coaster look like?