Physics midterm question: crushing-fender car

Physics 205A Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 7.13

A car is retrofitted with special fenders that would completely crush on impact, such that it would be stationary (and not rebound) after crashing into the wall. Discuss why this retrofitted car would experience a smaller magnitude crash impulse than a car that would rebound slightly after crashing into a wall. (Assume that the addition of special fenders do not substantively change the mass of the car.) Explain your reasoning using the properties of impulse and momentum.

Solution and grading rubric:
  • p:
    Correct. Since impulse is the change in momentum, discusses how the retrofitted car undergoes a smaller momentum change than a car that rebounds off of the wall.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have slightly garbled definition of impulse-momentum theorem, but argument is conceptually sound.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. At least understands that ∆v magnitude is greater for rebounding car in analyzing the car crashes with regards to momentum change.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at applying impulse and momentum concepts, but may have involved force and/or elapsed time in argument.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Discussion based on how momentum or kinetic energy is "absorbed" or "transmitted back" by crushing or rebounding fenders.
  • y:
    Irrelevant discussion/effectively blank.
  • z:

Grading distribution:
Sections 70854, 70855
Exam code: midterm02fR3q
p: 20 students
r: 8 students
t: 7 students
v: 11 students
x: 7 students
y: 0 students
z: 0 students

A sample "p" response (from student 0524):

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