# Test 3 - Version 018 TEST03 TSOI(58160 This print-out...

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Version 018 – TEST03 – TSOI – (58160) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points The fgure below shows a rigid 3-mass system which can rotate about an axis perpendicular to the system. The mass oF each connecting rod is negligible. Treat the masses as parti- cles. The x -axis is along the horizontal direction with the origin at the leFt-most mass 7 kg. 7 kg 7 kg 7 kg 4 m 4 m x The masses are separated by rods oF length 4 m, so that the entire length is 2 (4 m). Determine the x -coordinate oF the center oF mass For the three-mass system with respect to the origin. 1. 3.07692 2. 5.06667 3. 5.0 4. 4.16667 5. 3.46154 6. 2.66667 7. 1.52941 8. 4.0 9. 4.28571 10. 2.35714 Correct answer: 4 m. Explanation: ±irst fnd the center oF mass. Defne the origin to coincide with the Far leFt mass M . X CM = m i x i m i = (7 kg)(0 ) (7 kg) + (7 kg) + (7 kg) + (7 kg)(1 (4 m) (7 kg) + (7 kg) + (7 kg) + (7 kg)(2 (4 m) (7 kg) + (7 kg) + (7 kg) = 21 kg 21 kg (4 m) = 4 m . 002 10.0 points A wheel starts From rest at t = 0 and rotates with a constant angular acceleration about a fxed axis. It completes the frst revolution in 6 . 5 s. How long aFter t = 0 will the wheel com- plete the second revolution? 1. 6.08112 2. 9.89949 3. 9.61665 4. 7.9196 5. 7.21249 6. 2.82843 7. 11.8794 8. 8.76812 9. 9.19239 10. 3.67696 Correct answer: 9 . 19239 s. Explanation: Let : t 1 = 6 . 5 s , θ 1 = 1 rev , and θ 2 = 2 rev . The wheel starts From rest, so θ = θ 0 + 1 2 αt 2 = 1 2 αt 2 t 2 . Thus θ 2 θ 1 = t 2 2 t 2 1 t 2 = r θ 2 θ 1 t 1 = r 2 rev 1 rev (6 . 5 s) = 9 . 19239 s . 003 10.0 points

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Version 018 – TEST03 – TSOI – (58160) 2 Two identical balls (labelled A and B) move on a frictionless horizontal tabletop. Initially, ball A moves at speed v A, 0 = 10 m / s while ball B is at rest ( v B, 0 = 0). The two balls collide oF-center, and after the collision ball A moves at speed v A = 6 m / s in the direction θ A = 53 from its original velocity vector: 10 m / s A before B after 6 m / s A 0 m/s b b 53 Which of the following diagrams best repre- sents the motion of ball B after the collision? 1. after 8 m / s B 53 b 2. after 4 m / s B 37 b 3. 0 m/s B b after 4. 6 m / s B after b 5. after 6 m / s B 53 b 6. after 4 m / s B 53 b 7. 4 m / s B after b 8. after 8 m / s B 37 b correct 9. after 6 m / s B 37 b 10. 8 m / s B after b Explanation: Because we are given both the speed and the direction of ball A after the collision, the problem can be solved in terms of momentum conservation only. Indeed, there are no (horizontal) external forces acting on the two balls, so their net (horizontal) momentum vector is conserved during the collision: V P net = mV v A, 0 + mV v B, 0 [before] = mV v A + mV v B [after] and since V v B, 0 = V 0 (ball B is initially at rest), V v A + V v B = V v A, 0 .
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Test 3 - Version 018 TEST03 TSOI(58160 This print-out...

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