Physics final exam problem: spring-loaded cart collision

Physics 205A Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 6.11, Problem 7.43, Comprehensive Problem 7.71

A 0.30 kg cart is held against a spring that is compressed by 0.040 m. After the 0.30 kg cart is released from the spring, it travels horizontally with a velocity of +0.45 m/s and collides and sticks together with a 1.50 kg cart that was initially at rest. Ignore friction, drag and other external forces during this brief collision. Find (a) the spring constant of the spring, and (b) the final velocity of the two stuck-together carts. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.


Solution and grading rubric:

• p:
  Correct. Applies (a) mechanical energy conservation to find spring constant of spring, and applies (b) momentum conservation to find final velocity of stuck-together carts.
• r:
  Nearly correct, but includes minor math errors. Appropriate conservation laws applied for both (a)-(b).
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Appropriate conservation law applied for one of (a) or (b) with correct or nearly correct result, other typically has misapplied conservation law (using momentum conservation when only mechanical energy is conserved, or kinetic energy conservation when only momentum is conserved).
• 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
Exam code: finalPr0p
p: 6 students
r: 6 students
t: 22 students
v: 14 students
x: 1 student
y: 2 students
z: 0 students

A sample "p" response (from student 8821):
A sample "t" response (from student 9603), succesfully finding only the spring constant of the spring:
Another sample "t" response (from student 1101), successfully finding only the final collision of the stuck-together carts: