**ERIC Number:**EJ1177773

**Record Type:**Journal

**Publication Date:**2018-May

**Pages:**4

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0031-921X

**EISSN:**N/A

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.

Descriptors: Physics, Science Instruction, Teaching Methods, Video Technology, Scientific Principles, Comparative Analysis, Equations (Mathematics)

American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://aapt.scitation.org/journal/pte

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

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