Sol_Problem_of_the_Week_&acirc;€“_12

# Sol_Problem_of_the_Week_&acirc;€“_12 - Fundamental...

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Problem of the Week – 12 A rod of length L and negligible mass is attached to a disk of mass M and radius R. A string is wrapped around the disk, and you pull on the string with a constant force F. Two small balls each of mass m slide along the rod with negligible friction. The apparatus starts from rest, and when the center of the disk has moved a distance d, a length of string s has come off the disk, and the balls have collided with the ends of the rod and stuck there. The apparatus slides on a nearly frictionless table. Here is a view from above: System: disk-rod-mass assembly and string. Surroundings: agent providing force F. a) At this instant, what is the speed v of the center of the disk?

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Unformatted text preview: Fundamental Principle: Work done on point-particle system. ! K trans = ! F net " # d ! r cm = Fd = 1 2 ( M + 2 m ) v 2 v = 2 Fd M + 2 m b) At this instant, the angular speed of the disk is ω . How much thermal energy has been produced? Fundamental Principle: Work done on real system. W ext = ! K trans + ! K rot + ! E thermal F ( d + s ) = Fd + 1 2 ( 1 2 MR 2 + 2 m L 2 " # \$ % & ' 2 ) ! 2 + ! E thermal ! E thermal = Fs ( 1 2 ( 1 2 MR 2 + 2 m L 2 " # \$ % & ' 2 ) 2 c) In the next short amount of time Δ t, by how much will the angular speed change ( Δω )? Fundamental Principle: Angular Momentum Principle. ! ! ! t = ! ! L = I ! " ! = RF ! t I , I = 1 2 ( MR 2 + mL 2 )...
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Sol_Problem_of_the_Week_&acirc;€“_12 - Fundamental...

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