Physics quiz question: same momentum, different mass objects

Physics 5A Quiz 4, spring semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 7.10

[Version 1]
Two objects with different masses have the same magnitude momentum. The object with __________ mass has more kinetic energy.
(A) less.
(B) more.
(C) (There is a tie.)
(D) (Not enough information is given to determine this.)

Correct answer: (A)

Starting with the condition that two objects with different masses M > m, and different speeds, v < V, respectively, have the same momentum magnitudes:

M·v = m·V,

then:

(1/2)·M·v = (1/2)·m·V.

Since v < V, then:

(1/2)·M·v = (1/2)·m·V,

(1/2)·M·v·v < (1/2)·m·V·V,

such that:

(1/2)·M·v² < (1/2)·m·V²,

K_M < K_m,

and so the object with the smaller mass m will have more (translational) kinetic energy than the object with the larger mass M.

Student responses
Sections 4987, 4988
(A) : 4 students
(B) : 9 students
(C) : 5 students
(D) : 0 students

[Version 2]
Two objects with different masses have the same magnitude momentum. The object with __________ mass has less kinetic energy.
(A) less.
(B) more.
(C) (There is a tie.)
(D) (Not enough information is given to determine this.)

Correct answer: (B)

Student responses
Sections 4987, 4988
(A) : 12 students
(B) : 3 students
(C) : 3 students
(D) : 0 students