Physics final exam question: bullet embedding in block

Physics 5A Final Exam, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 7.44

[20 points.] A 0.075 kg bullet is shot horizontally and collides with a 2.00 kg block of wood that is initially stationary. The bullet embeds in the block and the block slides along a horizontal surface for 1.25 m. The coefficient of kinetic friction between the block and surface is 0.400. Determine the original speed of the bullet. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. The collision between the bullet and block is a perfectly inelastic collision, and uses conservation of momentum to relate the initial velocity v_1,i of the bullet with the final velocity of the bullet-block system v_12,f. As the bullet-block system slides across the surface, applies energy conservation to relate the amount of kinetic energy contained in v_12,f with the negative work done by kinetic friction. Finds that v_12,f = 3.13 m/s, and v_1,i = 86.6 m/s.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. At least systematically divides problem into momentum conservation and energy conservation segments, and serious attempt at connecting information and reduction of unknowns between the momentum and energy conservation equations.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically has one conservation law applied on a systematic manner, the other is problematic or missing.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Only one conservation law applied, and in a problematic manner (or equivalent amount of constructive effort).
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
p: 2 students
r: 5 students
t: 7 students
v: 15 students
x: 3 students
y: 1 student
z: 0 students

A sample of a "p" response (from student 7937) is shown below:
A nearly correct attempt (from student 6867) is a sample of an "r" response:
A "v" response (from student 6788) has a "WTF" ("what to find") moment: