20181115

Physics quiz question: Oregon Convention Center pendulum cable length

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

the longest pendulum currently in existence is at the Oregon Convention Center in Portland, OR, a 40 kg mass swinging on a cable with a period of 9.25 seconds.[*] At that location the magnitude of the acceleration due to gravity g is 9.82611 m/s2.[**] The length of the cable for this pendulum is:
(A) 4.53 m.
(B) 14.5 m.
(C) 21.3 m.
(D) 209 m.

[*] Martin Beech, The Pendulum Paradigm: Variations on a Theme and the Measure of Heaven and Earth, BrownWalker Press (2014), p. 42.
[**] wolframalpha.com/input/?i=gravitational+acceleration+portland,+or.

Correct answer (highlight to unhide): (C)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass. Since the period T = 9.25 s and gravitational constant g = 9.82611 m/s2 are known, the length L can then be solved for:

L = g·(T/(2·π))2,

L = (9.82611 m/s2)·((9.25 s)/(2·π))2 = 21.2963585648... m,

or to three significant figures, the length of the pendulum cable is 21.3 m.

(Response (A) is g·((2·π)/T)2; response (B) is g·T/(2·π); response (C) is ((g·T)/(2·π))2.)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 1 student
(B) : 3 students
(C) : 46 students
(D) : 2 students

Success level: 88%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

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