Physics midterm question: student on scale

Physics 205A Midterm 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.37

A Physics 205A student who weighs 550 N is standing on a stationary bathroom scale that weighs 30 N. Newton's __________ law tells you that these two forces are equal in magnitude and opposite in direction:

Weight of the student (the force of Earth pulling on the student).
Normal force of the floor on the scale.

(A) first.
(B) second.
(C) third.
(D) (These forces are not equal in magnitude and/or opposite in direction.)
(E) (Not enough information is given.)

Correct answer: (D)

Newton's first law applies to both the student and the scale, as they are both stationary.

There are two forces acting on the student: the weight of the student (the downwards force of Earth pulling on the student), and the normal force of the scale upwards on the student. These two forces must be equal in magnitude due to Newton's first law.

There are three forces acting on the scale: the weight of the scale (the downwards force of Earth pulling on the scale), and the normal force of the student downwards on the scale, and the normal force of the floor upwards on the scale. These three forces must be sum to zero due to Newton's first law. Thus the upwards normal force of the floor on the scale must be equal in magnitude to the sum of the two downwards forces (weight of the scale, and the downwards normal force of the student on the scale), so the upwards normal force of the floor on the scale must be greater in magnitude than the downwards normal force of the student on the scale.

The downwards normal force of the student on the scale is equal in magnitude (and opposite in direction) to the upwards normal force of the scale on the student, due to Newton's third law. Since the upwards normal force of the scale on the student is equal to the magnitude of the downwards weight of the student (due to Newton's first law, as discussed above), then the upwards normal force of the floor on the scale must be greater in magnitude than the weight of the student.

N_{floor on scale} > N_{student on scale} = N_{scale on student} = w_student.

Sections 70854, 70855
Exam code: midterm01sWFf
(A) : 27 students
(B) : 5 students
(C) : 8 students
(D) : 17 students

Success level: 30%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80