PHYS310_Exam3_solutions

PHYS310_Exam3_solutions - PHYS 310 Exam3 Name Problem 1(30...

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Unformatted text preview: PHYS 310: Exam3 November 21, 2011 Name: Problem 1 (30 points) Two weights of mass m 1 and m 2 are tied to the ends of a light inextensible cord. The cord passes over a rough pulley of radius a and moment of inertia I . Find the accelerations of the weights, assuming m 1 >m 2 and ignoring friction in the axle of the pulley. Energy is conserved: 2 2 2 1 2 2 1 1 1 1 2 2 2 2 x m x m x I m gx m gx E + + +- = & & & 1 2 2 1 2 I m xx m xx xx m gx m gx a + + +- = &&& &&& &&& & & ( 29 1 2 1 2 2 m m g x I m m a- = + + && There is a typo in this solution to this end of chapter in the solution manual. On the first line it should be an a instead of 2 in the kinetic energy of the pulley. Alternate solution: write equations of motion for each of the 3 bodies M 1 g-T 1 =m 1 a c (T 1-T 2 )a=I d ϖ /dt T 2-m 2 g=m 2 a c Where T 1 and T 2 are the tensions in the two sections of the string, and a c is the acceleration of the bodies Add them all up to get the same solution as above m 1 m 2 x a PHYS 310: Exam3 November 21, 2011...
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This note was uploaded on 12/07/2011 for the course PHYS 310 taught by Professor Jones,m during the Fall '08 term at Purdue.

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PHYS310_Exam3_solutions - PHYS 310 Exam3 Name Problem 1(30...

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