Physics final exam problem: kinetic energy loss of completely inelastic collision

Physics 205A Final Exam, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 7.43, Comprehensive Problem 7.71

A 0.20 kg cart launched off of a spring in the +x direction with a velocity of +0.11 m/s collides with a heavier 1.00 kg cart that is initially at rest. The carts stick together after the collision. Neglect drag and friction. Demonstrate numerically that kinetic energy is not conserved for this collision. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.


Solution and grading rubric:

• p:
  Correct. Applies (1) conservation of momentum to determine final velocity of the stuck-together cards, and (2) demonstrates numerically that kinetic energy is not conserved.
• r:
  Nearly correct, but includes minor math errors. One of the two points (1)-(2) correct, other is problematic/incomplete.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Both points (1)-(2) problematic/incomplete, or one point correct while other is missing.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying some conservation law.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying conservation laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finaln0M3
p: 15 students
r: 3 students
t: 19 students
v: 19 students
x: 1 students
y: 2 students
z: 2 students

A sample "p" response (from student 0000), finding the final velocity of the conjoined carts from momentum conservation, and shows that the initial total kinetic energy is not equal to the final total kinetic energy:
A sample "p" response (from student 1313), also finding the final velocity of the conjoined carts from momentum conservation, but instead showing that the loss of kinetic energy of the first cart is not equal to the gain in kinetic energy of the second cart: