Physics final exam problem: spring-shot sliding box

Physics 205A Final Exam, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 6.26, Comprehensive Problem 6.85

[20 points.] A spring (k = 56.0 N/m) is used to shoot a 0.0250 kg block. Initially the spring is compressed by 0.100 m when the block is held stationary against it. The block loses contact with the spring when the spring returns back to its unstretched length. The block then slides up along a hill. What is the speed of the block when it is at the top of the hill, 0.700 m above the launch point of the spring? Neglect friction. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Identifies relevant terms in energy balance equation (K_tr, U_grav, U_elas), and solves for v_f given that W_nc = 0.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Typically has sign error, or decimal place error, or dropped variable.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Some attempt at energy conservation, but with missing or misapplied energy terms, resulting in the velocity of the block as it is released from the spring, or the velocity of the block if it fell 0.700 m starting from rest.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some progress at setting up energy conservation terms.
  
• 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 70854, 70855
p: 9 students
r: 16 students
t: 5 students
v: 7 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student 7220):

A sample "t" response (from student 1942):

Another sample "t" response (from student 4567):