Physics quiz question: stretching fishing lines

Physics 205A Quiz 6, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Conceptual Question 11.4, Problems 11.1, 11.3

Eileen Delhi

Trilene® XL Super Strong fishing line (Young's modulus 2.0×109 N/m2) and Eagle Claw® Sportfisher fishing line (Young's modulus 3.1×109 N/m2) have the same 10.0 m length [*]. The Trilene® fishing line has a cross-sectional area 1.8 times that of the Eagle Claw®. Both fishing lines are stretched with a tension force of 98 N. The __________ fishing line will stretch more.
(A) Trilene®.
(B) Eagle Claw®.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] S. Ottolini, G. Halpin, P. LaBruzzo, "Tensile Strength of Fishing Line," santarosa.edu/~yataiiya/E45/PROJECTS/Tensile%20Strength%20of%20Fishing%20Line%20Power%20Point.ppt.

Correct answer (highlight to unhide): (B)

Hooke's law for the Trilene® and Eagle Claw® fishing lines are given by:

(F/ATri) = YTri·(∆LTri/L),
(F/AEagle) = YEagle·(∆LEagle/L),

where tension F and the original, unstretched length L are the same for both fishing lines. The Trilene® fishing line has a cross-sectional area 1.8× that of the Eagle Claw® fishing line:

ATri = 1.8·AEagle.

The amount that the Trilene® fishing line will be stretched is given by:

LTri = (F·L)/(ATri·YTri),

LTri = ((98 N)·(10.0 m))/((1.8·AEagle)·(2.0×109 N/m2)),

LTri = (2.7×10–7 m3)/AEagle.

Similarly, the amount that the Eagle Claw® fishing line will be stretched is given by:

LEagle = (F·L)/(AEagle·YEagle),

LEagle = ((98 N)·(10.0 m))/((AEagle)·(3.1×109 N/m2)),

LEagle = (3.1×10–7 m3)/AEagle.

Thus this sample of Eagle Claw® fishing line will stretch more than the Trilene® fishing line sample.

Sections 70854, 70855, 73320
Exam code: quiz06eAg7
(A) : 13 students
(B) : 49 students
(C) : 2 students
(D) : 0 students

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46

No comments: