Physics midterm problem: categorizing a cart collision

Physics 205A Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.90 kg cart traveling in the +x direction at 0.45 m/s collides with a 0.15 kg cart that is initially at rest. The carts are not stuck together after the collision. After the collision, the 0.90 kg cart continues traveling in the +x direction at 0.35 m/s. Ignore friction, drag and other external forces during this brief collision. Find (a) the final velocity of the 0.15 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_f2 = +0.60 m/s of the 0.15 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 translational kinetic energy is conserved, and finds that since it is not conserved, this collision must be inelastic.
  
• r:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Has correct v_f2 from momentum conservation, and at least some attempt at testing for translational kinetic energy conservation.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Application of momentum conservation, but v_f2 is incorrect, with little or no test of kinetic energy conservation.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02r3iN
p: 28 students
r: 7 students
t: 13 students
v: 4 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 1408):