HW5 Solution

HW5 Solution - lew (dl9564) hk5 Opyrchal (41104) 1 This...

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Unformatted text preview: lew (dl9564) hk5 Opyrchal (41104) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points A thin uniform cylindrical turntable of radius 2 . 9 m and mass 23 kg rotates in a horizontal plane with an initial angular speed of 11 rad / s. The turntable bearing is frictionless. A clump of clay of mass 9 . 7 kg is dropped onto the turntable and sticks at a point 1 . 7 m from the point of rotation. Find the angular speed of the clay and turntable. Correct answer: 8 . 52811 rad / s. Explanation: Let : R = 2 . 9 m , M = 23 kg , = 11 rad / s , and m = 9 . 7 kg . Basic Concepts: summationdisplay vector L = dvector ext dt K = K f- K i = Q . From conservation of the angular momentum it follows that L i = L f or I i = I f f , where I i = 1 2 M R 2 = 1 2 (23 kg) (2 . 9 m) 2 = 96 . 715 kg m 2 . Similarly, I f = I i + mx 2 = 96 . 715 kg m 2 + (9 . 7 kg) (1 . 7 m) 2 = 124 . 748 kg m 2 . Finally, f = I i I f = (96 . 715 kg m 2 ) (124 . 748 kg m 2 ) (11 rad / s) = 8 . 52811 rad / s . 002 (part 2 of 2) 10.0 points Calculate the loss of energy to thermal en- ergy. Correct answer: 1314 . 88. Explanation: K i = 1 2 I i 2 = 1 2 (96 . 715 kg m 2 ) (11 rad / s) 2 = 5851 . 26 J . K f = 1 2 I f 2 f = 1 2 (124 . 748 kg m 2 ) (8 . 52811 rad / s) 2 = 4536 . 38 J . Therefore, K = K f- K i = (4536 . 38 J)- (5851 . 26 J) =- 1314 . 88 J . Since the question asks for the loss of energy, we take the negative of this number. 003 10.0 points A solid cylinder of mass M = 11 kg, radius R = 0 . 43 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 3 kg and initial...
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HW5 Solution - lew (dl9564) hk5 Opyrchal (41104) 1 This...

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