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ERIC Number: EJ1177773
Record Type: Journal
Publication Date: 2018-May
Pages: 4
Abstractor: As Provided
ISSN: ISSN-0031-921X
Newtonian Analysis of a Folded Chain Drop
Mungan, Carl E.
Physics Teacher, v56 n5 p298-301 May 2018
Consider a chain of length L that hangs in a U shape with end A fixed to a rigid support and free end E released from rest starting from the same initial height (call it y = 0) as A. Figure 1 sketches the chain after end E has fallen a distance y. Points O and A are assumed to be close enough to each other and the chain flexible enough that the radius of curvature r at the bottom point C can be taken to be negligibly small (compared to the length of the chain). The problem is to compare the speed of descent v(y) = dy/dt of the free end E of the chain to the speed v[subscript free] ( y ) = [crossed through square root 2gy] of a free-falling point mass that has descended the same distance y. If v(y) > v[subscript free] (y) for all y > 0, then, in a race to fall any arbitrary distance Y (where 0 < Y < L), the chain end E will always beat a simultaneously released point mass, because the fall time t for E will be shorter than t[subscript free] for the point ] ( y ) . (1) Experimentally, this outcome of the race is observed in a "Veritasium" video.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A