Moment of Inertia Pulley Friction Incline Doohickey of Doom [AP physics & editio

Question

Moment of Inertia Pulley Friction Incline Doohickey of Doom [AP physics & edition] Your inconsiderate and unruly physics teacher sets the Moment of Inertia Pulley Friction Incline Doohickey of Doom in front of you and gives you this information... Mass of block = mass of pulley = 3.0 kg The Pulley is magically frictionless, has radius of 0.40 m, and has a massless string wrapped around itself that is attached to the block in such a way that it is parallel to the incline plane. Oh... by the way... the string is also inextensible. The incline has and angle of 30 degrees and a coefficient of static friction = 0.30 and a coefficient of kinetic friction = 0.20 Your physics teacher places the block a distance L = 2.0 m from the end of the incline hands you a stopwatch and says: "Time how long it takes the Mock to reach the bottom of the doohickey ." With growing dread you take the stopwatch. Your lightning fast reflexes record a time of 1.25 seconds. "Now... find the moment of inertia of the pulley and be quick about it!" the teacher commands. Not wishing to show weakness or fear in front of your peers. you proudly boust. "You don't scare me you vile fiend! I'll do better then that! I will: Calculate the pulleys moment of inertia. Calculate the tension in your silly massless-inextennsible string. Determine both the horizontal and vertical forces that are required to keep year magical frictionless pulley in static equilibrium while the doohickey is in operation. And, for good measure. I will draw a sketch of the inner workings of this magical frictionless pulley. Be it disk, or hoop, or some other creature entirely!

Explanation / Answer

the coefficient friction µs = 0.3 and µk = 0.2 the length of the block moves L = 2.0m
From the figure    I = 1/2 MR^ = (0.5)(3)(0.4)^2
   = 0.24 kgm^2
from Newton 's laws
Fnet = [mgsin? - µmgcos? -T ]*L = 0 mgsin? - µmgcos? -T = 0 T =(3)(9.8) [ sin30 - (0.3)(cos30)]
   = 7.06 N The vertical forces    N - mgcos? = 0

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