Physics quiz question: energy stored in compressed spring

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

A replacement coil spring for a Lincoln Town Car[*] has a spring constant of 740 N/m, and is mounted such that it can be compressed horizontally. When this spring is compressed by 0.020 m, it stores __________ of elastic potential energy.
(A) 0.15 J.
(B) 0.30 J.
(C) 7.4 J.
(D) 15 J.

[*] streetsideauto.com/p/moog-9114/

Correct answer (highlight to unhide): (A)

The change in elastic potential energy is given by:

∆PE_elas = (1/2)·k·∆(x²) = (1/2)·k·(x_f² – x₀²),

where the spring was initially uncompressed (x₀ = 0) and then compressed by x_f = –0.020 m from equilibrium, such that:

∆PE_elas = (1/2)·(740 N/m)·((–0.020 m)² – (0)²) = 0.148 J,

or to two significant figures, the spring stores 0.15 J of elastic potential energy.

(Response (B) is k·x_f²; response (C) is (1/2)·k·x_f; response (D) is k·x_f, which is the force required to compress the spring by 0.020 m.)

Sections 70854, 70855
Exam code: quiz06Ho0k
(A) : 27 students
(B) : 1 student
(C) : 5 students
(D) : 12 students

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73