Physics midterm problem: categorizing a cart collision

Physics 205A Midterm 2, fall semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 7.47

A 0.300 kg cart traveling in the +x direction at 0.20 m/s collides with a 0.500 kg cart that is initially at rest. The carts are not stuck together after the collision. After the collision, the 0.500 kg cart (that was initially at rest) travels in the +x direction at 0.15 m/s. Neglect drag and friction. Find (a) the final velocity of the 0.300 kg cart, and (b) classify this collision as elastic, inelastic, or completely inelastic. Show your work and explain your reasoning.


Solution and grading rubric:

• p:
  Correct. Finds final speed of the 0.300 kg cart, using conservation of momentum (as there is neither drag nor friction), v_f1 = -0.050 m/s. 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 misinterprets collision as being completely inelastic, but at least applies momentum conservation to find the correct v_f1 for the case where the carts are stuck together, then shows that kinetic energy was not conserved for this stuck-together collision.
  
• 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 inelastic solely 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
p: 7 students
r: 2 students
t: 31 students
v: 7 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 5446), testing for kinetic energy conservation after applying momentum conservation: