Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Example 8.12
"All Disks Roll the Same," 1Q1035.movUniversity of Minnesota, School of Physics & Astronomy
http://groups.physics.umn.edu/demo/mechanics/1Q1035.html
Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the end of their learning cycle:
A V-8 can and a Diet Pepsi can (both empty) are placed at the top of an inclined plane, and are released such that they begin to roll down at the same time. (This experiment is set-up, but not yet demonstrated yet for the students until after answers have been compiled.)
[0.6 participation points.] Which empty can do you think will reach downhill first?
(A) V-8 can.
(B) Soda can.
(C) (They will reach the bottom of the slope at approximately the same time.)
(D) (I'm lost, and don't know how to answer this.)
Sections 0906, 0907
(A) : 11 students
(B) : 21 students
(C) : 5 students
(D) : 0 students
Correct answer: (C)
The energy conservation equation for a rolling ring (which approximates an empty beverage can) is:0 = (1/2)*m*v_f^2 + (1/2)*I*w_f^2 + M*g*h,
where I = m*R^2, such that:
v_f = sqrt(g*h).
Thus both cans will have the same speed as they reach the bottom of the inclined plane, which can plausibly be reasoned to mean that they reach the bottom at the same time.
2 comments:
Physics 5A, Spring Semester 2008
Cuesta College, San Luis Obispo, CA
(Asked after speed as a function of hill height was derived from energy conservation.)
Sections 4987, 4988
(A) : 7 students
(B) : 9 students
(C) : 12 students
(D) : 1 student
N.B.: Performing this experiment with cans is critically dependent on relative starting positions of the pull-tabs/openings; several runs may be necessary to show that while there appears to be a can that "wins" the downhill derby, there is no consistent winner with many resets and re-runs.
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