Physics quiz question: comparing work done by friction in stopping sliding boxes

Physics 205A Quiz 4, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.9

Two boxes of the same mass and initial speed slide across two different horizontal floor surfaces, and each slide different distances to come to a complete stop. The box that slid a shorter distance to stop had __________ work done against it by kinetic friction, compared to the box that slid a longer distance.
(A) less.
(B) the same amount of.
(C) more.
(D) (Not enough information is given.)

Correct answer: (B)

Starting with the energy balance equation:

W_nc = ∆KE_tr + ∆PE_grav + ∆PE_elas,

where ∆PE_grav = 0 (as there is no change in elevation), ∆PE_elas = 0 (as there are no springs), such that:

W_nc = ∆KE_tr,

W_nc = (1/2)·m·v_f² – (1/2)·m·v₀²,

where the final speed v_f  of both boxes is zero; and since both boxes also had the same initial speed v₀, then the same amount of (negative) work was done by friction on each box.

Sections 70854, 70855, 73320
Exam code: quiz04w3Rc
(A) : 15 students
(B) : 17 students
(C) : 33 students
(D) : 0 students

Success level: 26%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49