Physics quiz question: tractor-trailer crash impulse

Physics 205A Quiz 4, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Fig. 4.59. Sloshing of Tractor-Trailer Cargo (Right View)"
Texas A&M Transportation Institute
tti.tamu.edu/documents/9-4973-1.pdf

A computer simulation of a tractor-trailer vehicle (mass of 3.5×10⁴ kg) colliding at a speed of 22 m/s with a stationary concrete bridge support predicts that it takes 0.35 s to come to a complete stop[*]. If the concrete bridge support had "impact attenuators" (plastic barrels filled with sand[*]), the tractor-trailer vehicle would take a longer time to come to a complete stop. This would __________ the magnitude of the impulse exerted on the tractor-trailer vehicle.
(A) decrease.
(B) not change.
(C) increase.
(D) (Not enough information is given.)

[*] C. Eugene Buth, William F. Williams, Michael S. Brackin, Dominique Lord, Srinivas R. Geedipally, and Akram Y. Abu-Odeh, "Analysis of Large Truck Collisions with Bridge Piers: Phase 1. Report of Guidelines for Designing Bridge Piers and Abutments for Vehicle Collisions," Texas Transportation Institute (May 2010), p. 39, tti.tamu.edu/documents/9-4973-1.pdf.
[**] traffixdevices.com/products/attenuators.

Correct answer (highlight to unhide): (B)

The impulse J can be calculated as the initial-to-final change in momentum:

J = ∆p = m·∆v,

where ∆v = v_f – v₀.

The initial velocity vector is v₀ = +22.0 m/s (traveling in the forwards direction), and the final velocity vector is v_f = 0 m/s (coming to a complete stop). Then:

J = (3.5×10⁴ kg)·((0 m/s) – (+22.0 m/s)) = –770,000 N·s,

or to two significant figures, the magnitude of the impulse is 7.7×10⁵ N·s (and the "–" sign indicates that it is in the backwards direction).

If the same tractor-trailer with same initial velocity of +22.0 m/s instead collides with an "impact attenuator" and comes to a complete stop over a longer duration of time, the impulse on the tractor-trailer would be the same as colliding and coming to a stop without it. However, the longer duration of time to come to a complete stop in the case of the impact attenuator would decrease the net force on the tractor-trailer, as:

J = ΣF·∆t.

Sections 70854, 70855
Exam code: quiz04th1R
(A) : 32 students
(B) : 9 students
(C) : 10 students
(D) : 0 students

Success level: 18%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.16