the falling chain
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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 - PowerPoint PPT PresentationTRANSCRIPT
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The Falling Chain
Luu ChauKayla Chau
Jonathan Bernal
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Question: What falls faster?
• What falls faster? – The end of a vertically hanging folded chain– A free falling object (tennis ball)
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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
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a: End of chain
b: Steel Ring (object)
c: Mathematical model of a freefalling object
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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
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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
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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
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Chain Equations
•By assuming that energy is conserved, we can come up with equations for velocity, acceleration, and time
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Free Falling Object
•We assume no air resistance when modeling this experiment on Matlab
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Object Equations
•We will use these equations to model the free-falling object
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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