Physics midterm question: bounce or splat impulse?

Physics 8A Midterm 3, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q8.1

[10 points.] A gun is fired straight down at a steel plate. Is the impulse on the plate from a single bullet impact greater if the bullet bounces off of the plate, or if the bullet squashes and sticks to the plate, or is the impulse the same in either case? Explain your answer using properties of impulse and momentum.

(Cf. Young and Freeman, University Physics, 11/e, Discussion Question 8.13.)

Solution and grading rubric:

• p = 10/10: Correct.
  Impulse is equal to delta(p), where p_i is down, and p_f is either zero (stuck to plate), or up (bounces up off plate). Respectively then the impulse on the plate is then equal to -p_i or -2*p_i (if the collision is elastic), thus the impulse on the plate is greater when the bullet bounces off the plate. This is irregardless of the time of the impact.
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Utilizes impulse = delta(p) relation with understanding of initial and final momentum directions, but argument is garbled or contradicts correct set-up.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some attempt at incorporating impulse and momentum in discussion.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on energy or angular momentum considerations, or a choice that has no explanation.
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
p: 2 students
r: 7 students
t: 16 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

A sample (incorrect) student response (from J. H.) is shown below. At least some attempt was made to relate this question to a real-life experience. This was graded as a "t" category response.