Physics final exam problem: hot bullet into ice block

Physics 205A Final Exam, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 14.102

[20 points.] A 0.44 kg lead slug leaves a rifle at a temperature of 155 degrees C and travels at a speed of 190 m/s until it hits a 20.0 kg block of ice at 0 degrees C and comes to a rest within it. Determine how much ice will melt. Show your work and explain your reasoning.

(Specific heat of lead is 0.13 kJ/(kg*K); specific heat of ice is 2.1 kJ/(kg*K); latent heat of fusion for water is 333.7 (kJ/kg) ; specific heat of water is 4.19 kJ/(kg*K).)

Solution and grading rubric:

• p = 20/20:
  Correct. The kinetic energy of the bullet that is lost (7,942 J) as it comes to a complete stop, along with the heat it gives up as it cools down to 0 degrees C (8,866) is equal to the heat absorbed by the ice as it melts (16,808 J), and the resulting mass of ice melting is found to be 0.0504 kg.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Does not include the kinetic energy of the bullet.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• 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:
Sections 30880, 30881
p: 2 students
r: 5 students
t: 22 students
v: 9 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 5225):

A sample "r" response (from student 0008), with a kJ to J conversion error:

Another sample "r" response (from student 1830), with similar kJ to J conversion errors, but no explicit calculation for the amount of ice melted:

Another sample "r" response (from student 1990), with similar kJ to J conversion errors, coming to the conclusion that the entire ice block would melt:

Another sample "r" response (from student 6447), again with similar kJ to J conversion errors and concluding that the entire ice block would melt:

A sample "t" response (from student 1807), with no kinetic energy of the bullet:

Another sample "t" response (from student 1991), again with no kinetic energy of the bullet: