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Rollercoasters and Centripetal Force

Rollercoasters and Centripetal Force. By Edward Greve. Question: BIG or small ?. Two types of spheres – big and small - are tested around a loop, theoretically and experimentally. Which works better? Why?. The Scenario:. R. T. r. t. 90. 90. H. D. L. 45. The Numbers:. BIG.

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Rollercoasters and Centripetal Force

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  1. Rollercoasters and Centripetal Force By Edward Greve

  2. Question: BIG or small? Two types of spheres – big and small - are tested around a loop, theoretically and experimentally. Which works better? Why?

  3. The Scenario: R T r t 90 90 H D L 45

  4. The Numbers: BIG small • K = 1/2 Iw^2 • I = 2/5 mR^2 • w= v/r • K= 1/5mv^2 + 1/2m/v^2 = 7/10mv^2 • K = 1/2 Iw^2 • I = 2/5 mR^2 • w= sqrt(2)v/r • K= 2/5mv^2 + 1/2m/v^2 = 9/10mv^2

  5. Centripetal Force • The centripetal acceleration must be greater than or equal to the acceleration due to gravity, or the sphere will fall off the loop. a = v^2/L >= 9.81 m/s^2 L = 19.5 cm v >= 1.4 m/s

  6. More Numbers: BIG small • mgH = mgD + 7/10 mv^2 • gH = gD + 7/10 v^2 • v >= 1.4 m/s • D = 39 cm • H >= 52 cm • H = 55 cm • mgH = mgD + 9/10 mv^2 • gH = gD + 7/10 v^2 • v >= 1.4 m/s • D = 39 cm • H >= 57 cm • H = 73 cm Experimental Results:

  7. Answers at last! • The numbers show that the BIG ball works better than the small ball. • More of the small ball’s total energy is used in keeping it rotating because it has a smaller lever arm (t ~ r < T ~ R =~ 1). • More of the BIG ball’s total energy is used linearly, thus, the BIG ball is the better choice to get around the loop more easily.

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