Physics quiz question: CERN proton Lorentz factor

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.55(a)

The CERN Proton Synchrotron Booster in Switzerland (http://cdsmedia.cern.ch/img/CERN-Brochure-2008-001-Eng.pdf) is able to accelerate protons up to a speed of 0.916c, as measured from a stationary reference frame. What is the Lorentz factor γ for protons at this speed?
(A) 1.09.
(B) 1.19.
(C) 2.49.
(D) 3.45.

Correct answer: (C)

The Lorentz factor is given by:

γ = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.916c/c)^2) = 2.49.

Response (A) is 1/(v/c); response (B) is 1/(v/c)^2; response (D) is 1/sqrt(1 - (v/c)).

Student responses
Section 31988
(A) : 2 students
(B) : 3 students
(C) : 7 students
(D) : 0 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80