## 20170106

### Physics final exam problem: rubber vs. aluminum bullets shot at wooden blocks

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

On an online discussion board[*] a claim was made that a stationary wood block will have a faster final speed if a rubber bullet fired at it bounces off of it, compared to a slower final speed for the wooden block if an aluminum bullet fired at it fully embeds itself inside it. Assume the rubber bullet[**] and the aluminum bullet have the same mass of 0.075 kg and the same initial horizontal speed of 150 m/s, fired at stationary wood blocks that each have the same mass of 8.0 kg. Verify this expected result by determining (a) the final speed of the wood block, after the rubber bullet rebounds with a speed of 143 m/s; and (b) the final speed of the wood block, after the aluminum bullet is fully embedded in the block. Ignore friction, drag, and external forces. Show your work and explain your reasoning using properties of collisions, impulse, momentum, and momentum conservation.

[*] answers.yahoo.com/question/index?qid=20121011172202AAobQUe.
[*] litfld.net/starlight-less-lethal-ammo-product-specifications/.

Solution and grading rubric:
• p:
Correct. Determines/discusses:
1. the final velocity of the wood block in the (partially) inelastic collision with the rubber bullet from applying momentum conservation;
2. the final velocity of the wood block in the completely inelastic collision with the aluminum bullet from applying momentum conservation; and makes some argument that the results are consistent with the original claim.
• r:
Nearly correct, but includes minor math errors. (Typically has correct final velocity of the block for the completely inelastic collision, but neglects to give the bullet a negative final velocity for the partially inelastic collision.)
• t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying momentum conservation to find the final velocity of the blocks.
• x:
Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than momentum conservation (typically kinetic energy conservation, when neither of these collisions are elastic)
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 10 students
r: 19 students
t: 1 student
v: 5 students
x: 10 student
y: 4 students
z: 0 students

A sample "p" response (from student):