DATA:
Radius of primary axis (measured from center of ride to center of car cluster): ________Radius of secondary axis (measured from center of car cluster to center of car): ________
Indicate on diagram above the directions of rotation (as seen from above)
Time for one rotation of the total ride: ________
Time for one rotation of the car cluster: ________
Maximum lateral acceleration (aL): __________ g's (measured on the ride at full speed)
Minimum lateral acceleration (aL): __________ g's (measured on the ride at full speed)
In the problem that follows, ignore the fact that the entire ride is set at an angle to the horizontal. Consider the ride as if it were running in a horizontal manner.
PROBLEM
This is a place where your expertise in calculus will shine through. Good luck.
- Given the rotation speed and the radius of the car cluster,
write an equation to describe the velocity vs. time for an
individual car in the frame of reference of the car cluster.
- Given the rotation speed and the radius of the car cluster
on the total ride platform, write an equation to describe the
velocity vs. time for a car cluster in the frame of reference
of the stationary ground around the ride.
- Combine the results of your two equations to predict the
overall motion of an individual car relative to the stationary
ground.
- Sketch the graph that is formed by this equation. (If
possible, plot it on a graphing calculator, if you brought
one, to check it out.)
- Find the maximum and minimum accelerations (dv/dt) of an
individual car as given by your equations.
- Compare your measured accelerations with the calculated values.
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Updated 1/27/2012