Physics midterm problem: bullet embedding into block

Physics 205A Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 7.43, 7.44

A 0.0036 kg Nosler® Ballistic Tip V-Shok .223 Remington bullet[*] is shot horizontally with a speed of 988 m/s and collides into a 2.6 kg block of wood. The bullet embeds itself in the block, and the block with embedded bullet together slide along a horizontal frictionless surface. What is the final kinetic energy of the sliding block and embedded bullet system? Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.

[*] federalpremium.com/products/compare/rifle_compare.aspx.

Solution and grading rubric:
  • p:
    Correct. Applies momentum conservation to the perfectly inelastic collision between bullet and block to find the final velocity of bullet/block, and then calculates the final kinetic energy of bullet/block.
  • r:
    Nearly correct, but includes minor math errors. Momentum conservation applied to successfully find the final velocity of bullet/block, problematic kinetic energy calculation.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only momentum conservation applied to successfully find the final velocity of bullet/block. No kinetic energy calculation.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Garbled attempt at momentum conservation, may or may not have kinetic energy calculation.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Does not apply momentum conservation.
  • y:
    Irrelevant discussion/effectively blank.
  • z:

Grading distribution:
Sections 70854, 70855
Exam code: midterm02fR3q
p: 24 students
r: 4 students
t: 5 students
v: 8 students
x: 7 students
y: 0 students
z: 0 students

A sample "p" response (from student 4816):

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