Test #2-solutions

Test #2-solutions - Version 052/AADBA Test#2...

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Version 052/AADBA – Test #2 – Antoniewicz – (56445) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 6.0 points L b Mg Two identical springs are in parallel. Each spring has one oF its ends attached to the ceiling and its other end attached to a weight. The mass oF the springs is negligible. Consider the situation in which the weight has a mass M and the system is stretched by a length b. Choose correct statements below Ia. The sti±ness oF one spring is M g 4 b Ib. The sti±ness oF one spring is M g 2 b IIa. The amount oF stretch in one spring is b 2 IIb. The amount oF stretch in one spring is b IIIa. The amount oF Force along one spring is M g 2 IIIb. The amount oF Force along one spring is M g. 1. Ia, IIb, IIIb 2. Ib, IIa, IIIb 3. Ia, IIa, IIIa 4. Ia, IIb, IIIa 5. Ib, IIb, IIIb 6. Ia, IIa, IIIb 7. Ib, IIb, IIIa correct 8. Ib, IIa, IIIa Explanation: The sti±ness oF the 2-spring system For the present setup is by defnition k = M g b . With the parallel setup, the Force is equally shared between the two identical springs, i.e. each spring experiences a Force oF F = M g 2 . Since the total stretch is given to be b, with the parallel arrangement, each spring stretches by the same amount. The sti±ness oF one spring is M g 2 b = M g 2 b . 002 6.0 points A piece oF iron is Fastened on top oF a block oF wood ²oating in water. IF the block is inverted so the iron is below the block oF wood, would the wood ²oat at the same level, lower, or higher? 1. Higher, because there is a buoyant Force acting on the iron now. correct 2. It would ²oat lower, because the iron displaces water and the overall water level would rise. 3. It depends on the ratio oF iron and wood volumes. 4. It would ²oat at the same level. Explanation: The iron-wood unit displaces its combined

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Version 052/AADBA – Test #2 – Antoniewicz – (56445) 2 weight and the same volume of water whether the iron is on top or the bottom. When the iron is on top, more wood is in the water. When the iron is on the bottom, less wood is in the water. 003 6.0 points A ball of mass 350 g hangs from a spring whose stiFness is 115 N / m. A string is attached to the ball and you pull the string to the right, so that the ball hangs motionless, as shown in the ±gure. In this situation, the spring is stretched, and its length is 14 cm. What would be the relaxed length of the spring, if it were detached from the ball and laid on a table? Use g = 9 . 8 m / s 2 . 14 cm 8 cm 1. 0.11465 2. 0.112717 3. 0.101251 4. 0.108795 5. 0.131846 6. 0.123672 7. 0.0951667 8. 0.12037 9. 0.0961802 10. 0.103656 Correct answer: 0 . 103656 m. Explanation: Let θ be the angle between the spring and the vertical, and let s represent the amount by which the spring has stretched under the given circumstances. Then sin θ = 8 cm 14 cm and cos θ = 11 . 4891 cm 14 cm , where 11 . 4891 cm is obtained from the Pythagorean theorem. The vertical compo- nent of the spring tension must null out the ball’s weight, so, using Hooke’s Law, we can write mg = k s s cos θ s = k s 14 cm 11 . 4891 cm = (350 g)(9 . 8 m / s 2 )(14 cm) (115 N / m)(11 . 4891 cm) = 0 . 0363444 m .
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Test #2-solutions - Version 052/AADBA Test#2...

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