Physics quiz question: pendulum and mass-spring periods on Earth, and on the moon

Physics 205A Quiz 6, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 10.8

A 0.50 kg point mass is hung from a string to make a pendulum of period 1.0 s on Earth, and a 0.50 kg mass is attached to a horizontal spring to make a mass-spring system of period 1.0 s on Earth. Neglect friction and drag. If this pendulum and this mass-spring system are both taken to the moon (where g = 1.62 m/s²) and used there, the __________ will have a longer period.
(A) pendulum.
(B) mass-spring system.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The period of a pendulum is given by:

T = 2·π·√(L/g),

where the moon's lower gravitational constant would make the period of the pendulum longer than on Earth (as the length L of the string does not change).

The period of a mass-spring system is given by:

T = 2·π·√(m/k),

and since the mass m and the spring constant k are the same on the moon as on Earth, the period of the mass-spring system does not change.

Sections 70854, 70855
Exam code: quiz06How3
(A) : 35 students
(B) : 3 students
(C) : 8 students
(D) : 0 students

Success level: 76%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45