Physics quiz question: semi-tractor truck colliding with bridge

Physics 205A Quiz 4, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.13(a)

"Truck Gets Wedged Under Raleigh Bridge (Thursday, May 25, 2014)"
(ABC11iwitness photo)
abc11.com/traffic/truck-gets-wedged-under-bridge/61259/

A semi-tractor truck (mass 12,000 kg) traveling at 9.0 m/s (20 mph) collides with a low overhang bridge, coming to a complete stop in 0.75 s. As a result of crashing into the bridge, the semi-tractor truck loses __________ of kinetic energy.
(A) 0 J.
(B) 1.1×10⁵ J.
(C) 1.4×10⁵ J.
(D) 4.9×10⁵ J.

Correct answer (highlight to unhide): (D)

The change in (translational) kinetic energy for the semi-tractor truck is given by:

∆KE_tr = (1/2)·m·(v_f² – v₀²),

where the final speed of the semi-tractor truck is zero, such that:

∆KE_tr = (1/2)·(1.2×10⁴ kg)·((0 m/s)² – (9.0 m/s)²) = –486,000 J,

or to two significant figures, –4.9×10⁵ J; thus the semi-tractor truck loses 4.9×10⁵ J of kinetic energy.

(Response (B) is the magnitude of the external impulse (or change in momentum) ∆p = m·(v_f – v₀); and response (C) is the magnitude of the average net force exerted on the semi-tractor truck ΣF_ext = ∆p/∆t.)

Sections 70854, 70855, 73320
Exam code: quiz04iSs5
(A) : 3 students
(B) : 14 students
(C) : 24 students
(D) : 25 students

Success level: 38%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.24