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The Falling Chain

The Falling Chain. Luu Chau Kayla Chau Jonathan Bernal. Question: What falls faster?. What falls faster? The end of a vertically hanging folded chain A free falling object (tennis ball). Physical Experiment. Camera takes multiple pictures in a given time increment

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The Falling Chain

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  1. The Falling Chain Luu Chau Kayla Chau Jonathan Bernal

  2. Question: What falls faster? • What falls faster? • The end of a vertically hanging folded chain • A free falling object (tennis ball)

  3. Physical Experiment • Camera takes multiple pictures in a given time increment • After first flash from camera, detector switches open the circuit • Circuit gives charge to magnets holding a steel ring (object) and end of chain • As steel ring and end of chain fall, camera takes multiple pictures, marking position

  4. a: End of chain b: Steel Ring (object) c: Mathematical model of a freefalling object

  5. End of Chain Wins • On a physical level, the end of a chain falls faster than a free falling object • A down-pulling force at the fold of the chain is created giving the chain extra pull as it falls

  6. Chain Fold • Close-up representation of the fold in a falling chain • We neglect individual link oscillations to further explain the down-pulling force created on the fold • This force creates an equal & opposite reactive force pointing downward, adding to the gravitational force

  7. Mathematical Level • Chain divided into parts: • -Falling section of chain (La) • -Motionless section of chain (Lb) • As time goes on • -La will decrease • -Lb will increase

  8. Chain Equations • By assuming that energy is conserved, we can come up with equations for velocity, acceleration, and time

  9. Free Falling Object • We assume no air resistance when modeling this experiment on Matlab

  10. Object Equations • We will use these equations to model the free-falling object

  11. Work Cited • M. Schagerl, A. Steindl, W. Steiner, and H. Troger, “On the paradox of the free falling folded chain,” Acta Mech. 125, 155-168 1997. • W. Tomaszewski and P. Pieranski, “Dynamics of ropes and chains I. The fall of the folded chain,” New J. Phys. 7, 45-61 2005. • W. Steiner and H. Troger, “On the equations of motion of the folded inextensible string,” Z. Angew. Math. Phys. 46, 960-970 1995. • M.G. Calkin and R. H. March, “The dynamics of a falling chain I,” Am. J. Phys. 57, 154-157 1989. • T. McMillen and A. Goriely. “Shape of a Cracking Whip,” Phys. Rev. Lett, 88(24) 2002

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