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Experimentation and Analysis By the Inertias

THE DYNAMIC CAROUSEL. Experimentation and Analysis By the Inertias. Objectives. Measure centripetal acceleration at various distances from the center Compared measured acceleration to acceleration found by another method Find and analyze vertical acceleration of horsies. V t. V t.

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Experimentation and Analysis By the Inertias

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  1. THE DYNAMIC CAROUSEL Experimentation and Analysis By the Inertias

  2. Objectives • Measure centripetal acceleration at various distances from the center • Compared measured acceleration to acceleration found by another method • Find and analyze vertical acceleration of horsies

  3. Vt Vt ac = ω2r Vt r v ac Vt r v ac Ac vs. r

  4. Our Results: Red: larger radius Green: smaller radius Outside mean: .435 Inside mean: .486

  5. Why our data turned out a little bit different than we had predicted • We Da Know? • We can only assume some things: • The ride itself was traveling at different speeds • The linear accelerometer was pointed a little off center (measure less than true acceleration) • More people were getting on the ride and none were getting off (additional mass)

  6. Another Method • We were also able to calculate the acceleration by timing the number of rotations at the carousel’s cruising speed • ac=ω2r • where ω ∽ (# of rotations)/(# of seconds) • Data • 45 seconds • 3 rotations • Results • Inside: .662 m/s2 • Outside: 1.19 m/s2 • compared to measured • inside: .435 m/s2 • outside: .486 m/s2

  7. 3 rotations 2 π radian 6 π radians = = .419 radians / sec. 45 seconds 1 rotation 45 seconds How It’s Done ac= ω2 r aci = (.419)2 (3.77) = .662 aco = (419)2 (6.77) = 1.19

  8. Whoa Horsie! • We recorded the vertical acceleration of a horse. • Our Hypothesis: • Above equilibrium (half way point) • Acceleration is negative greater than gravity • Below equilibrium • Acceleration less than gravity • When velocity equals zero at top and bottom • acceleration equals gravity

  9. Motion of horse Acc - The red line is gravity, above the line the magnitude of acceleration is greater than gravity below the line magnitude of acceleration is less than gravity. Acc +

  10. Improvements • More Brains • More time to plan and prepare • More runs to collect precise data • Careful placement of data collecting instruments and experiment appropriate equipment

  11. Motion of horse Acc - Acc + What did we Learn? ac = ω2r 1 2

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