Physics quiz question: Young's modulus of stretched wire

Physics 205A Quiz 6, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 10.4

A wire of length 3.000 m with a cross section area of 2.2e-6 m^2 stretches by 0.012 m when a load of 900 N is hung from it. What is the Young's modulus for this wire?
(A) 1.6e+6 Pa.
(B) 1.5e+7 Pa.
(C) 4.1e+8 Pa.
(D) 1.0e+11 Pa.

Correct answer: (D)

Hooke's law is given by:

(F/A) = Y*(delta(L)/L).

Solving for Y,

Y = (F*L)/(A*delta(L)) = (900 N)*(3.000 m)/((2.2e-6 m^2)*(0.012 m)) = 1.02272727...e+11 = 1.0e+11, to two significant figures.

Response (A) is F*delta(L)/(A*L); response (B) is F*delta(L)*L/A; response (C) is F/A = stress.

Student responses
Sections 70854, 70855
(A) : 5 students
(B) : 1 student
(C) : 2 students
(D) : 40 students

Success level: 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.69

Student responses
Section 72177
(A) : 0 students
(B) : 1 student
(C) : 1 student
(D) : 10 students

Success level: 83%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33