Physics quiz question: Cadillac ATS and BMW 328i collision

Physics 205A Quiz 4, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 7.47

(Ignore friction, drag, and other external forces during this brief collision.) A 2013 Cadillac ATS (mass 1,577 kg) traveling 12 m/s hits a stationary 2013 BMW 328i (mass 1,545 kg)[*]. Neither driver applies the brakes. Based solely on the information given, __________ must be conserved.
(A) momentum.
(B) translational kinetic energy.
(C) (Both of the above choices.)
(D) (None of the above choices.)

[*] "Cadillac ATS curb weight 3477 pounds; BMW 328i curb weight: 3390 pounds," media.caranddriver.com/files/2013-bmw-328i-vs-2013-cadillac-ats2013-cadillac-ats-and-2013-bmw-328i-comparo.pdf.

Correct answer (highlight to unhide): (A)

Negligible net external force and brief time duration for this collision makes the external impulse on this system zero, such that momentum is conserved. Since no information is given whether there is permanent deformation of both cars after the collision, it is not possible to determine if this is an elastic collision (such that translational kinetic energy is conserved) or an inelastic or completely inelastic collision (such that translational kinetic energy is not conserved). Without additional information regarding the resulting permanent deformation (if any) of the two cars after the collision, only momentum can be said to be conserved.

Sections 70854, 70855
Exam code: quiz04Bmw3
(A) : 37 students
(B) : 3 students
(C) : 11 students
(D) : 1 student

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.87


Robbie McCabe said...

Why/How does the "brief time duration" affect the external impulse on a system?

Patrick M. Len said...

External impulse on a system during a collision is the net force of the external world on the system, times the time duration of the collision. Even if the forces on the system from the external world are quite large, collisions are typically very, very brief processes (milliseconds or so), thus effectively making the external impulse negligible.

(Another justification for making the external impulse negligible is that the external forces on the system (friction, drag) are also very, very small compared to the internal forces the colliding objects exert on each other during the collision.)