Physics midterm problem: penny on turntable

Physics 205A Midterm 1, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 5.80(b)

[20 points.] A Physics 205A student places a penny (mass 2.50 g) on an old phonograph turntable, at a distance of 10.0 cm from the center. The coefficient of static friction between the penny and the turntable is 0.19. The turntable starts with an initial angular velocity of 33.3 rpm, and speeds up to 45.0 rpm. Will the penny stay on the turntable? Neglect air resistance. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Argues that the penny will slide off the turntable before reaching its final speed of 45 rpm, by either solving for the required radial (centripetal) net force and showing that it is greater than the maximum static friction force; or by solving for the rotational speed that the penny would still remain on the turntable (when its static friction force is maxed out), and showing that it is less than 45 rpm = 4.7 rad/s. Free-body diagram, identification of forces, application of Newton's laws (first law, and second law for uniform circular motion), and interpretation of results is clearly shown.
  
• 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. At least has free-body diagram with magnitudes of forces calculated, and/or rational attempt at applying Newton's second law for uniform circular motion to these force magnitudes.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Typically calculates w_i, w_f, f_s, and/or m*r*w^2, but does not implement Newton's second law for uniform circular motion.
  
• 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: 8 students
r: 1 students
t: 9 students
v: 20 students
x: 6 students
y: 1 student
z: 0 students

A sample of a "p" response, demonstrating that the angular speed that the penny would begin to slide off the turntable is less that the final angular speed (from student 1977):
Another "p" response (from student ), demonstrating that the maximum static friction force is less than the centripetal net force required to keep the penny on the turntable at its final angular speed: