Physics quiz question: box sliding down ramp at constant speed

Physics 5A Quiz 3, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 4.49

[3.0 points.] A 75.0 kg box is sliding down a ramp at a constant velocity. The ramp makes an angle of 15.0 degrees above the horizontal direction. Which one of the following forces has the greatest magnitude?
(A) Kinetic friction force on the box.
(B) Weight of the box.
(C) Normal force of the ramp on the box.
(D) (Not enough information is given to determine this.)

Correct answer: (B)

The weight of the box has a magnitude m*g = 735 N. Since it is sliding down the ramp at constant speed (along a constant direction), then Newton's first law applies, which means that the forces acting on the book must sum to zero, according to the Newton's law flowcharts.

This means that the (tilted) x-component of the weight force is equal and opposite to the kinetic friction force, thus f_k = m*g*sin(15.0 degrees) = 190 N. The (tilted) y-component of the weight force is equal and opposite to the normal force, thus N = m*g*cos(15.0 degrees) = 710 N.

Student responses
Sections 4987, 4988
(A) : 5 students
(B) : 29 students
(C) : 5 students
(D) : 3 students