Physics final exam problem: block sliding downhill into spring

Physics 205A Final Exam, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 6.87

A 0.45 kg block is 1.20 m above the base of a slope, where it starts with an initial speed. At the bottom of the slope is a horizontal k = 60 N/m spring, which is compressed by 0.55 m from equilibrium when the block comes (momentarily) to a stop. What was the initial speed of the block? Neglect friction and drag. Show your work and explain your reasoning using the properties of energy conservation.

Solution and grading rubric:

• p:
  Correct. Sets up an energy conservation equation with changes in gravitational potential energy, translational kinetic energy, and elastic potential energy summing to zero (as there is no non-conservative work), and solves for the initial speed of the block.
  
• r:
  Nearly correct, but includes minor math errors. Typically forgets to square quadratic terms, or has sign error.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least applies energy conservation, but with non-conservative work done, a missing energy term, etc.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Calculations of energy terms, but does not tie them together in an energy conservation equation.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than energy conservation.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 30880, 30881
p: 10 students
r: 11 students
t: 7 students
v: 7 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 1990):
A sample "r" response (from student 0506), with a sign error for -9.80 m/s² (which should be positive in calculating scalar quantities such as gravitational potential energy):
Another sample "r" response (from student 2411), with two sign errors:
Another sample "r" response (from student 4278), forgetting to square the quadratic terms for spring potential energy:
A sample v" response (from student 4444), with a plea for clemency, but at least demonstrating some attempt at applying energy conservation concepts: