Physics quiz question: stress and strain of different cross-section bars

Physics 5A Quiz 6, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 10.4(b)

[3.0 points.] A cylindrical steel bar of radius 2.50 cm is compressed by the application of forces of magnitude 1.50 x 10^3 N at each end. What magnitude forces (at each end) would be required to compress by the same amount a steel bar of the same length, but a radius of 1.25 cm?
(A) 375 N.
(B) 750 N.
(C) 1.06 x 10^3 N.
(D) 1.50 x 10^3 N.

Correct answer: (A)

Hooke's law relating stress (F/A) and strain (delta(L)/L)) is:

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

where Y is the Young's modulus for the material. Since the radius is reduced by a factor of two, then the area is reduced by a factor of four, such that the force required to cause the same amount of strain in this smaller cross section bar would be one-fourth the original force. Response (B) is one-half of the original force, while response (C) is sqrt(2) = 0.707 times the original force.

Student responses
Sections 4987, 4988
(A) : 8 students
(B) : 19 students
(C) : 3 students
(D) : 3 students