Physics quiz question: time dilated pulse

Physics 205B Quiz 7, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 26.5, Problem 26.5.

A Physics 205B student has a resting pulse of 1 second per beat. She then takes a ride aboard a spacecraft traveling at a constant velocity of 0.100c away from Earth. While the spacecraft is moving, the resting pulse of the Physics 205B student is __________ 1 second per beat, according to Earth observers.
(A) longer than.
(B) shorter than.
(C) exactly equal to.
(D) (Not enough information is given.)

Correct answer: (A)

The relevant time interval is the pulse of the Physics 205B student. The proper time interval delta(t_0) for her pulse is 1 second, as measured in her own reference frame (the spacecraft). The observed time interval delta(t) for her pulse is measured from Earth, which is at rest outside of the reference frame of the spacecraft. Then the relation between the two time intervals is given by:

delta(t) = gamma*delta(t_0);

and since gamma = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.100c/c)^2) = 1/sqrt(1 - 0.0100) = 1/sqrt(0.9900) = 1/0.9950 = 1.005, then:

delta(t) = 1.005*(1 second/pulse) = 1.005 seconds/pulse.

Student responses
Section 70856
(A) : 8 students
(B) : 2 students
(C) : 1 student
(D) : 0 students

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.33