Physics quiz question: femur compression

Physics 205A Quiz 6, fall semester 2015
Cuesta College, San Luis Obispo, CA

An average femur bone (Young's modulus 9.4×10⁹ N/m²) has a length of 0.48 m and an approximate cross-sectional area of 1.72×10^–3 m², and reportedly can support a maximum 2.4×10⁴ N of force.[*][**] When this force is applied, the femur would compress by:
(A) 2.1×10^–9 m.
(B) 9.1×10^–9 m.
(C) 7.2×10^–8 m.
(D) 7.1×10^–4 m.

[*] "30 times the weight of an adult," orthopaedicsone.com/display/Review/Femur.
[**] "Weight of average adult: 178 lbs," wolfr.am/8dc2Ohi7.

Correct answer (highlight to unhide): (D)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

such that the amount that the femur would be compressed is:

∆L = (F·L)/(A·Y),

∆L = ((2.4×10⁴ N)·(0.48 m))/((1.72×10^–3 m²)·(9.4×10⁹ N/m²)),

∆L = 0.0007125185552 m,

or to two significant figures, the femur would compress by 7.1×10^–4 m.

(Response (A) is (F·L·A)/Y; response (B) is (F·A)/(L·Y); response (C) is A/F.)

Sections 70854, 70855, 73320
Exam code: quiz06m45S
(A) : 3 students
(B) : 0 students
(C) : 3 students
(D) : 67 students

Success level: 92%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.17