Physics quiz question: rope, pulley, suspended box

Physics 205A Quiz 3, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.50 kg box is suspended by use of an ideal pulley and rope. Neglect the weights of the pulley and rope. Newton's __________ law tells you that these two forces are equal in magnitude and opposite in direction:

Tension force of rope on the box.
Weight force of Earth on the box.

(A) first.
(B) second.
(C) third.
(D) (These forces are not equal in magnitude and/or opposite in direction.)

Correct answer (highlight to unhide): (A)

The box has two vertical forces acting on it:

Tension force of rope on the box (upwards).
Weight force of Earth on the box (m_box·g = 4.9 N, downwards).

Since the box is stationary, then according to Newton's first law the forces acting on it must sum to a net force of zero, and the tension force must also have a magnitude of 4.9 N. Thus weight and tension force are equal in magnitude and opposite in direction due to Newton's first law.

(Note that these two forces only satisfies one of the three components of the POF-OST-ITO mnemonic (cf. Light and Matter by Benjamin Crowley, lightandmatter.com):

POF: Pair of Opposite Forces (yes)
OST: Of Same Type (no, tension force and normal force))
ITO: Involving Two Objects (no, rope (anchor), box, and Earth)

Thus Newton's third law does not apply to these two forces, despite them being equal in magnitude and opposite in direction, as two forces must meet all three components of the POF-OST-ITO test to be related via Newton's third law.)

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 44 students
(B) : 4 students
(C) : 8 students
(D) : 0 students

Success level: 79%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67