Physics quiz question: work done on crate coasting up along ramp

Physics 205A Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA

A crate gradually decreases in speed, as it slides up along a ramp. The ramp is not frictionless. Identify the force(s) that do positive work on the crate.
(A) w.
(B) N.
(C) f_k.
(D) (Two of the above choices.)
(E) (All of the above choices.)
(F) (None of the above choices.)

Correct answer (highlight to unhide): (F)

The three forces acting on the crate are:

normal force N (perpendicular outwards from the ramp surface);
weight force w (vertically downwards);
friction force f_k (down along the ramp).

The definition of work done is W = F·s·cosθ, where the angle θ is measured between the direction of the force vector and the displacement vector (which points in the direction of motion) when drawn together "tail-to-tail."

The angle θ between the normal force N (perpendicular outwards from the ramp surface) and the displacement vector s (up along the ramp) is 90°, and since cos(90°) = 0, the normal force does zero work on the crate.

The angle θ between the kinetic friction force f_k (down along the ramp) and the displacement vector s (up along the ramp) is 180°, and since cos(180°) = –1, the kinetic friction force does negative work on the crate.

The angle θ between the weight force w (vertically downwards) and the displacement vector s (up along the ramp) is an obtuse angle between 90° and 180°, and since cosθ is negative for 90° < θ < 180°, the weight force also does negative work on the crate.


Thus there are no forces that do positive work on the crate.

Sections 70854, 70855, 73320
Exam code: quiz04w04K
(A) : 4 students
(B) : 22 students
(C) : 4 students
(D) : 11 students
(E) : 1 student
(F) : 30 students

Success level: 42%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.71