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Unformatted text preview: PHYS 172 – Fall 2010 Exam 3 Hand
written Portion (30 points total) Write down your recitation time: Name (Print): _______________________________________________________ Signature: __________________________________________________________ Day (either Wed, Th, Fri): PUID: _____________________________________________________________ Time: You will lose points if your explanations are incomplete, ___________________________ if we can’t read your handwriting, or if your work is sloppy. Hand
Written Problem: Object rolling down an inclined plane An object of mass M, radius R and moment of inertia I rolls without slipping (due to a frictional force of magnitude f, down an inclined plane of length L that is fixed to the ground as shown in the figure below. The object starts from rest a height h above ground level. When the object reaches the bottom of the inclined plane, its center of mass has fallen through a vertical distance h. Take the object as the system in the following analysis. h L θ
Ground Level A. (6 points) Treat the object as a point particle. In the space below, draw a force diagram on which all forces acting on the object are shown and labeled. Be certain to define a set of coordinate axes, X and Y. B. (6 points) What is the object’s translational kinetic energy when it reaches ground level? [Hint: Use the Energy Principle to answer this question to express your answer in terms of M, g, θ, L, and f .] C. (6 points) What is the object’s total kinetic energy (translational plus rotational) when it reaches ground level? D. (6 points) Use your answer to part C to find that the speed of the object 2 gh
when it reaches ground level is V =
. I
(1 +
)
MR 2 E. (6 points) The object’s moment of inertial can be represented as I = b ! M ! R 2 where b is a dimensionless number associated with the objects geometry. For example, b = 1 for a hoop, 2/5 for a sphere, ½ for a disk, etc. Express your answer in part D in terms of this expression for I, thereby showing that the final speed does not depend on either the object’s mass nor its radius. ...
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