Physics quiz question: concrete sample compression

Physics 205A Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

A concrete sample was (non-destructively) tested by compressing it with a stress of 9.9×10⁶ N/m²[*]. The Young's modulus of this concrete is 2.8×10¹⁰ N/m²[**]. If the concrete sample started with a height of 0.305 m, during testing it was compressed by:
(A) 1.1×10^–11 m.
(B) 1.1×10^–4 m.
(C) 3.5×10^–4 m.
(D) 5.5×10^–3 m.

[*] youtu.be/iCWsDHhbi9g.
[**] engineeringtoolbox.com/concrete-properties-d_1223.html.

Correct answer (highlight to unhide): (B)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

where the compressive stress (F/A) is given as 9.9×10⁶ N/m². The amount that sample would be compressed by will be:

∆L = (F/A)·(L/Y),

∆L = (9.9×10⁶ N/m²)·((0.305 m)/(2.8×10¹⁰ N/m²)),

∆L = 0.0001078392857 m,

or to two significant figures, the concrete sample would compress by 1.1×10^–4 m.

(Response (A) is L/Y; response (C) is the strain (∆L/L) = (F/A)/Y; response (D) is the volume of the concrete cylinder, which cannot be determined from the values given above.)

Sections 70854, 70855
Exam code: quiz06Ho0k
(A) : 4 students
(B) : 40 students
(C) : 1 student
(D) : 0 students

Success level: 89%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.27