20141005

Physics quiz question: book stacked on crate forces

Physics 205A Quiz 3, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.37(b)

A book and a crate are stacked on the floor, and both are motionless. The mass of the crate is greater than the mass of the book. The crate exerts an upwards force of 52 N on the book. Newton's __________ law tells you that these two forces are equal in magnitude and opposite in direction:
Upwards force of crate on book.
Downwards force of crate on floor.
(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 (highlight to unhide): (D)

The book has two forces acting on it:
Weight force of Earth on book (52 N, downwards).
Normal force of crate on book (52 N, upwards).
Because the book is stationary, these two forces are equal in magnitude (each 52 N) and opposite in direction, due to Newton's first law.

The crate has three forces acting on it:
Weight force of Earth on crate (some value greater than 52 N, downwards).
Normal force of book on crate (52 N, downwards).
Normal force of floor on crate (52 N plus weight force on crate, upwards).
Because the crate is stationary, the magnitudes of the two downward forces together must equal the magnitude of the upwards force, due to Newton's first law. From Newton's third law, the downwards normal force of the book on crate must be equal in magnitude and opposite in direction to the upwards normal force of the crate on book, so they are each 52 N.

Note that from Newton's third law, the normal force of the floor on crate (downwards) must be equal in magnitude (52 N plus weight force on crate) and opposite in direction to the normal force of the crate on the floor (upwards), as these two forces are an interaction pair. Thus the magnitudes and the directions of the two given forces are:
Normal force of crate on book (52 N, upwards).
Normal force of the crate on the floor (52 N plus weight force on crate, downwards).
So these two forces, while being opposite in direction, are not equal in magnitude. (In any case, they cannot be related by Newton's first law, as these two forces act on separate objects; and cannot be related by Newton's third law, as these two forces involve more than two objects.)

Sections 70854, 70855, 73320
Exam code: quiz03fkfs
(A) : 48 students
(B) : 3 students
(C) : 11 students
(D) : 10 students
(E) : 0 students
Success level: 14%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

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