Physics quiz question: Spire of Dubin pendulum length

Physics 205A Quiz 6, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Jim Larkin Statue and the Spire of Dublin"
Tony Webster

The Spire of Dublin is a monument containing internal pendulum systems to dampen vibrations. Its upper pendulum has a period of 3.6 s, and has a cable that suspends a 1,250 kg mass.[*][**][***] Neglect the mass of the cables. The upper pendulum has a cable length of:
(A) 1.8 m.
(B) 3.2 m.
(C) 3.8 m.
(D) 18 m.

[*] wki.pe/Spire_of_Dublin.
[**] sta.ie/perch/resources/lessons/a4dcclessoned.2.pdf.
[***] Matthew Wells, Skyscrapers: Structure and Design, Laurence King Publishing (2005), pp. 56-57.

Correct answer (highlight to unhide): (B)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass. Since the period T = 3.6 s and gravitational constant g = 9.80 m/s2 are known, the length L can then be solved for:

L = g·(T/(2·π))2,

L = (9.80 m/s2)·((3.6 s)/(2·π))2 = 3.217150223 m,

or to two significant figures, the length of the pendulum cable is 3.2 m.

(Response (A) is (1/(2·π))·√(m/g); response (C) is 2·π·√(T/g); response (D) is (1/(2·π))·√(m·g).)

Sections 70854, 70855, 73320
Exam code: quiz06rn3T
(A) : 2 students
(B) : 51 students
(C) : 2 students
(D) : 0 students

Success level: 93%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.36

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