quiz1031-solutions - Version 045/AACDB quiz1031 Demkov...

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Unformatted text preview: Version 045/AACDB quiz1031 Demkov (59910) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A cylindrical pulley with a mass of 5 . 1 kg, ra- dius of 0 . 883 m and moment of inertia 1 2 M r 2 is used to lower a bucket with a mass of 2 kg into a well. The bucket starts from rest and falls for 3 . 6 s. r M m How far does it drop? The acceleration of gravity is 9 . 8 m / s 2 . 1. 24.5 2. 25.6517 3. 41.2571 4. 19.6951 5. 13.1116 6. 27.9138 7. 30.2565 8. 17.8025 9. 13.4742 10. 36.0624 Correct answer: 27 . 9138 m. Explanation: Let : M = 5 . 1 kg , r = 0 . 883 m , m = 2 kg , and g = 9 . 8 m / s 2 . Let T be the tension in the cord and the angular acceleration of the wheel. Newtons equation for the mass m is mg- T = ma T = m ( g- a ) and for the disk T r = I ( mg- ma ) rh = parenleftbigg 1 2 M r 2 parenrightbigg parenleftBig a r parenrightBig 2 mg- 2 ma = M a 2 mg = ( M + 2 m ) a a = 2 mg M + 2 m From kinematics, since v = 0 , y = v t + 1 2 at 2 = 1 2 at 2 = 1 2 parenleftbigg 2 mg M + 2 m parenrightbigg t 2 = mg t 2 M + 2 m = (2 kg) (9 . 8 m / s 2 ) (3 . 6 s) 2 5 . 1 kg + 2 (2 kg) = 27 . 9138 m . 002 10.0 points A(n) 7 kg object moving at 9 m / s in the posi- tive x direction has a one-dimensional elastic collision with an object initially at rest. After the collision the object of unknown mass has a velocity of 8 m / s in the positive x direction. What is the unknown mass? 1. 8.75 2. 10.6667 3. 5.0 4. 2.1 5. 3.2 6. 1.4 7. 3.6 8. 6.3 9. 2.13333 10. 4.0 Correct answer: 8 . 75 kg. Explanation: Given: v 2 i = 0. From conservation of momentum, we have m 1 v 1 i = m 1 v 1 f + m 2 v 2 f m 1 ( v 1 i- v 1 f ) = m 2 v 2 f . (1) Version 045/AACDB quiz1031 Demkov (59910) 2 Because of elastic collision, energy is con- served. Therefore 1 2 m 1 v 2 1 i = 1 2 m 1 v 2 1 f + 1 2 m 2 v 2 2 f m 1 ( v 2 1 i- v 2 1 f ) = m 2 v 2 2 f m 1 ( v 1 i- v 1 f ) ( v 1 i + v 1 f...
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quiz1031-solutions - Version 045/AACDB quiz1031 Demkov...

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