Physics 8A Midterm 2, Spring Semester 2007Cuesta College, San Luis Obispo, CA
Physics 8A learning goal Q6.4
[20 points.] A thin ring of mass 2.40 kg and radius 0.100 m has a string wrapped around it that is pulled vertically upwards with an applied force 7.20 N in magnitude, and as a result it begins to roll (clockwise) to the right without slipping. Find the minimum coefficient of static friction that will allow this to happen.
(Cf. Young and Freeman, University Physics, 11/e, Problem 10.70.)
Solution and grading rubric:
- p = 20/20:
Correct. Draws an extended-body diagram, correctly identifying the directions and locations of F_applied, w, n, and f_s (horizontally to the right, at the point of contact). Then applies N1 in the y-direction, and finds that n = 16.3 N.
Applies N2 in the x-direction, and finds that
a_x = f_s/m = u_s*n/m.
Applies N2 rotational, and finds that
-m*(r^2)*alpha = -F_applied*r + f_s*r.
Constrains translational and rotational motion using a_x = r*alpha, and finds that
u_s = f/(2*(m*g) - F_applied) = 0.221. - 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 methodically applies Newton's laws for x, y, and rotations, and constrains translational and rotational motion, but typically demands n = mg, or has similar misapplications between using N1 or N2. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least some attempt at using Newton's laws, but with serious omissions or complications. - x = 4/20:
Implementation of ideas, but credit given for effort rather than merit. Typically sets up a diagram, and/or finds I = m*(r^2). - y = 2/20:
Irrelevant discussion/effectively blank. - z = 0/20:
Blank.
Grading distribution:
p: 1 student
r: 2 students
t: 12 students
v: 16 students
x: 5 students
y: 1 student
z: 1 student
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