Scramblers - AP

CENTRIFUGE

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 the diagram above the directions of rotation (as seen from above)

Time for one rotation of the total ride: ________

Time for one rotation of a car cluster: ________

Maximum lateral acceleration (a_L): __________ g's (measured on the ride at full speed)

Minimum lateral acceleration (a_L): __________ g's (measured on the ride at full speed)

In the problem which 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. This is a place where your expertise in calculus will shine through. Good luck.

PROBLEM

(1) Given the rotation speed and the radius of the car cluster, write an equation to describe the position vs. time for an individual car in the frame of reference of the car cluster.

(2) Given the rotation speed and the radius of the car cluster on the total ride platform, write an equation to describe the ride position vs. time for a car cluster in the frame of reference of the stationary ground.

(3) Add the results of your two equations to predict the overall position vs. time of an individual car relative to the stationary ground. [This equation can be plotted on a graphing calculator if you have one with you. Hint: polar coordinates.]

(4) Write the overall velocity vs. time equation for an individual car relative to the stationary ground.

(5) Find the maximum and minimum accelerations (dv/dt) of an individual car as predicted by your equation.

(6) Finally, compare your measured results with the calculated values.

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