Physics quiz question: stretching a wire

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 10.3

A "000" AWG-gauge copper wire[*] with Young's modulus of 1.2×10¹¹ Pa is 1.0 m long and has a cross-sectional area of 85.0 mm². If a weight of 300 N is hung from the wire, it will stretch:
(A) 3.6×10^–9 m.
(B) 2.1×10^–7 m.
(C) 2.8×10^–7 m.
(D) 2.9×10^–5 m.

[*] wki.pe/American_wire_gauge.

Correct answer (highlight to unhide): (D)

Hooke's law for elastic materials is given by:

(F/A) = Y·(∆L/L),

where the cross-sectional area of the wire is 85.0 mm² = 8.50×10^–5 m², such that the length that the amount the wire stretches is:

∆L = (F·L)/(A·Y)

∆L = ((300 N)·(1.0 m))/((8.50×10^–5 m²)·(1.2×10¹¹ Pa) = 2.941176471×10^–5 m,

or to two significant figures, ∆L = 2.9×10^–5 m.

(Response (A) is F·L·(1.2×10^–11 Pa); response (B) is F·L·(85.0 m²)/Y; and response (C) is A/F.)

Sections 70854, 70855
Exam code: quiz06How3
(A) : 2 students
(B) : 5 students
(C) : 9 students
(D) : 30 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.52