Physics midterm question: slide speed

Physics 205A Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 6.13

(Adapted from Eric Mazur, Peer Instruction: A User's Manual, Prentice Hall, 1997, p. 63.)

[10 points.] Consider two slides that start at the same height and end at the same lower height. Both slides have negligible friction, and neglect drag. Which slide would a Physics 205A student have the faster speed at the bottom, starting from rest? Explain your reasoning by using the properties of energy conservation.

Solution and grading rubric:

• p = 10/10:
  Correct. Uses energy conservation to show that the student will have
  the same speed at the bottom of either slide.
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least has methodical application of energy conservation.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit. Does not use energy conservation at all.
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
Sections 30880, 30881
p: 13 students
r: 6 students
t: 2 students
v: 5 students
x: 13 students
y: 0 students
z: 1 student

A sample of a "p" response (from student 0008):

Another sample "p" response (from student 0915):

One last sample "p" response (from student 0915), using perhaps much too many equations to make a simple point: