Physics quiz question: train buffer stop

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.13

"Rawie Buffer Stop 10 ZEB 8 Holanda Composição de 1430ton a 10 kmh"
Mundo Ferroviário
youtu.be/FmVSUl3cI5U

A 850,000 kg passenger train traveling at 4.2 m/s on a horizontal track pushes up against an end-of-track buffer stop[*]. As a result, the buffer stop brings the passenger train to a complete rest after traveling 7.0 m. Neglect friction and drag. The magnitude of the average force exerted by the buffer stop on the train is:
(A) 2.6×10⁵ N.
(B) 1.1×10⁶ N.
(C) 2.1×10⁶ N.
(D) 5.8×10⁷ N.

[*] "The buffer stop is designed to move up to 7 m to slow down a 850 t passenger train from 15 km/h," wiki.pe/File:Buffer_stop_zurich.jpg.

Correct answer (highlight to unhide): (B)

The non-conservative work done by the buffer stop (considered as an external agent outside of the train's energy systems) decreases the train's translational kinetic energy:

W_nc = ∆KE_tr,

where the work done is the product of the average force exerted and the displacement:

W_nc = F_av·s·cosθ,

such that the average force is:

F_av·s·cosθ = ∆KE_tr,

F_av = ∆KE_tr/(s·cosθ),

F_av = (1/2)·m·(v_f² – v₀²)/(s·cosθ),

F_av = = (1/2)·(850,000 kg)·((0 m/s)² – (4.2 m/s)²)/((7.0 m)·cos(180°)) = 1,071,000 N,

or to two significant figures, the magnitude of the force is 1.1×10⁶ N.

(Response (A) is (1/2)·m·v₀/(2·s); response (C) is m·v₀²/s; response (D) is m·g·s.)

Sections 70854, 70855
Exam code: quiz04Bmw3
(A) : 7 students
(B) : 20 students
(C) : 17 students
(D) : 7 students

Success level: 38%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80