Phys20_F08_MT2

Phys20_F08_MT2 - 3(25 pts An inclined plane of angle θ is...

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University of California, Santa Barbara Department of Physics Physics 20 Midterm 2 Fall 2008 1. (15 pts) A rope of mass m and length L is used to suspend a mass M from the ceiling of an elevator. The elevator is accelerating downward with acceleration a < g . Find the tension in the rope as a function of the distance y from the ceiling. 2. (25 pts) A mass M 1 on an inclined plane of angle θ is connected to a second mass M 2 , via massless frictionless string using a massless frictionless pulley, as shown. The coefficient of static friction between M 1 and the incline is μ S , and the kinetic coefficient of friction is μ K . M a g L m y
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a) Find the value of M 2 which is just sufficient to cause the mass M 1 to begin moving up the incline, if they are at rest, initially. b) Assuming the mass M 1 is moving up the plane, find the acceleration and the tension in the string.
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Unformatted text preview: 3. (25 pts) An inclined plane of angle θ is attached to a rotating platform as shown. A small mass is placed on the incline, a distance r from the axis of rotation. The coefficient of static friction between the mass and the incline is μ . Find the value of ω that will be just large enough to cause the mass to begin moving up the plane. (Remember ω = 2π/ T, where T is the period of rotation in seconds.) θ r ω 4. (35 pts) A frictionless rope of mass per unit length λ kg/m runs over a cylinder of radius R. The tension in the rope T, is constant, so the rope moves across the rod at constant speed v, as shown. Find the smallest value of T that will be sufficient to keep the rope in contact with the rod. (Hint: Consider a small piece of rope subtending a small angle δθ.) T T R v...
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Phys20_F08_MT2 - 3(25 pts An inclined plane of angle θ is...

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