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.[**]
In San Luis Obispo, CA, the magnitude of the acceleration due to gravity g is 9.80844 m/s2.[***]
If a similar pendulum were constructed in San Luis Obispo, CA, and set into the motion with the same amplitude, it would have a period __________ the period of the pendulum in Portland, OR.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)
[*] 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.
[***] wolframalpha.com/input/?i=gravitational+acceleration+san+luis+obispo,+ca.
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, and only on the length L of the cable (which is the same for both locations), and the gravitational acceleration constant g (which is different for these locations).
Since San Luis Obispo, CA has a slightly smaller gravitational acceleration constant (9.80844 m/s2) compared to Portland, OR (9.82611 m/s2), then the pendulum in San Luis Obispo, CA will have a slightly longer period compared to Portland, OR.
This can be shown quantitatively by writing out the pendulum period equations for both locations:
TPortland = 2·π·√(LPortland/gPortland),
TSLO = 2·π·√(LSLO/gSLO).
Since the cable length would be the same for both locations, then:
LSLO = LPortland,
and solving for the period for the pendulum in San Luis Obispo, CA:
gSLO·(TSLO/(2⋅π)2 = gPortland·(TPortland/(2⋅π)2,
gSLO·(TSLO/(
(TSLO)2 = (TPortland)2⋅(gPortland/gSLO) ,
TSLO = TPortland√(gPortland/gSLO),
TSLO = (9.25 s)·√((9.82611 m/s2)/(9.80844 m/s2)) = 9.2583282333... s,
which to three significant figures is 9.26 s, and thus longer than the period of the pendulum in Portland, OR.
Sections 70854, 70855
Exam code: quiz06POr7
(A) : 10 students
(B) : 10 students
(C) : 32 students
(D) : 0 students
Success level: 61%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58
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