Physics quiz question: work done on diagonally-pulled crate

Physics 205A Quiz 4, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.1

A rope that makes an angle of 35° above the horizontal drags a crate at constant speed across a floor that is not frictionless. The magnitude of the work done by friction on the crate is __________ the magnitude of the work done by the rope on the crate.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

Starting with the the energy balance equation:

W_nc = ∆KE_tr + ∆PE_grav + ∆PE_elas,

where ∆KE_tr = 0 (crate is being dragged at constant speed), ∆PE_grav = 0 (crate moves across a horizontal floor), and ∆PE_elas = 0 (no springs are involved), then:

W_nc = 0.

The vertical forces that act on the crate are weight (downwards) and the normal force of the floor (upwards), but since these are perpendicular to the displacement of the crate, each of these forces do zero work on the crate.

The horizontal kinetic friction force does negative work on the crate (as the angle between that force and displacement is 180°, where cos(180°) = –1), while the rope does positive work on the crate (as the angle between that force and displacement is 35°, where cos(35°) is a positive quantity).

However, since the net external work done on the crate is zero, then the (negative) work done by friction on the crate must have the same magnitude as the (positive) work done by the rope on the crate:

W_nc = 0,

W_friction + W_rope = 0.

Sections 70854, 70855
Exam code: quiz04iMpL
(A) : 31 students
(B) : 16 students
(C) : 4 students
(D) : 0 students

Success level: 31%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.36