Physics quiz question: steamrolling a golf ball

Physics 205A Quiz 6, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Steam Roller vs Golf Balls"
Crush
youtu.be/JGHcOd1kozc

Assume that a golf ball can be considered to be a cube with a cross-sectional area of 1.4×10^–3 m². A steam roller then applies 3.9×10⁴ N of downwards force on the golf ball, compressing it down to half of its original vertical height.[*][**] The overall Young's modulus for this golf ball is:
(A) 55 N/m².
(B) 2.0×10⁴ N/m².
(C) 2.8×10⁷ N/m².
(D) 5.6×10⁷ N/m².

[*] youtu.be/JGHcOd1kozc.
[**] wki.pe/Golf_ball.

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 A of the wire is 1.4×10^–3 m², the force F applied is 3.9×10⁴ N, and the ratio ∆L/L that the golf ball is compressed to is 1/2. The (overall) Young's modulus of the golf ball can then be solved for:

Y = (F/A)/(∆L/L),

Y = ((3.9×10⁴ N)/(1.4×10^–3 m²))/(0.5),

Y = 5.5714285714×10⁷ N/m²,

or to two significant figures, Y = 5.6×10⁷ N/m².

(Response (A) is F·A; response (B) is F/2; and response (C) is the applied stress F/A.)

Sections 70854, 70855, 73320
Exam code: quiz06rn3T
(A) : 3 student
(B) : 6 students
(C) : 9 students
(D) : 37 students

Success level: 69%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73