Physics final exam problem: categorizing a cart collision

Physics 205A Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 7.47, 7.49

A 0.40 kg cart traveling in the +x direction at 0.75 m/s collides with a 2.00 kg cart that is initially at rest. The carts are not stuck together after the collision. After the collision, the 2.00 kg cart (that was initially at rest) travels in the +x direction at 0.25 m/s. Ignore friction, drag and other external forces during this brief collision. Find (a) the final velocity of the 0.40 kg cart, and (b) classify this collision as elastic, inelastic, or completely inelastic. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.


Solution and grading rubric:

• p:
  Correct. Finds final speed v_f1 = –0.50 m/s of the 0.40 kg cart, using conservation of momentum (as there is negligible drag/friction for this brief collision). It is not known whether the carts are permanently deformed and/or energy was lost to thermal/sound systems, so collision could be either inelastic or elastic (but cannot be completely inelastic because the carts are not stuck together after the collision). Explicitly tests for whether or not kinetic energy is conserved, and finds that since kinetic energy is conserved, this collision must be elastic.
  
• r:
  Nearly correct, but includes minor math errors. As (p), but at least applies momentum conservation to find the correct v_f1, then tests for kinetic energy conservation.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Has correct v_f1 (may have magnitude only) from momentum conservation, but does not explicitly test for energy conservation, and attempts to identify collision as elastic or partially inelastic on the basis of no visible deformation, which is not explicitly stated.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Application of momentum conservation, but v_f1 is incorrect, with little or no test of kinetic energy conservation.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit. Discussion based on stated characteristics of collision, with no application or test of appropriate conservation laws.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalB0xs
p: 12 students
r: 13 students
t: 14 students
v: 8 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 3737), comparing the amounts of initial and final total kinetic energies:
A sample "t" response (from student 0361):
Another sample "t" response (from student 1776):
Yet another sample "t" response (from student 1995):