ch13-periodic-motion

# Ch13-periodic-motion - MasteringPhysics 10:22 PM Print View Print Introductory mechanics Chapter 13 Periodic Motion Due at 11:59pm on Tuesday

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12/9/08 10:22 PM MasteringPhysics Page 1 of 12 http://session.masteringphysics.com/myct [ Print View ] Introductory mechanics Chapter 13 - Periodic Motion Due at 11:59pm on Tuesday, December 9, 2008 View Grading Details Springs in Parallel In this problem you will study two cases of springs connected in parallel that will enable you to draw a general conclusion. Two springs in parallel Consider two massless springs connected in parallel. Springs 1 and 2 have spring constants and and are connected via a thin, vertical rod. A constant force of magnitude is being exerted on the rod. The rod remains perpendicular to the direction of the applied force, so that the springs are extended by the same amount. This system of two springs is equivalent to a single spring, of spring constant . Part A Find the effective spring constant of the two-spring system. Hint A.1 Free-body diagram Hint not displayed Part A.2 Extension of two springs Part not displayed Part A.3 Magnitude of Part not displayed Give your answer for the effective spring constant in terms of and . ANSWER: = Three springs in parallel Now consider three springs connected in parallel as shown. The spring constants of springs 1, 2, and 3 are , , and . [ Print ]

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12/9/08 10:22 PM MasteringPhysics Page 2 of 12 http://session.masteringphysics.com/myct The springs are connected by a vertical rod, and a force of magnitude is being exerted to the right. Part B Find the effective spring constant of the three-spring system. Give your answer in terms of , , and . ANSWER: = You have now seen that the general formula for the overall spring constant of a set of springs in parallel is the sum of the spring constants of the individual springs. You will see this again when you study electric circuits and learn about the total capacitance of capacitors in parallel. Springs in Series In this problem you will study two cases of springs connected in series that will enable you to draw a general conclusion. Two springs in series Consider two massless springs connected in series. Spring 1 has a spring constant , and spring 2 has a spring constant . A constant force of magnitude is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant . Part A What is the effective spring constant of the two-spring system? Hint A.1 Free-body diagram Hint not displayed Hint A.2 Free-body diagram for spring 2 Hint not displayed
12/9/08 10:22 PM MasteringPhysics Page 3 of 12 http://session.masteringphysics.com/myct Part A.3 Determine the extension of spring 2 Part not displayed Part A.4 Determine the extension of spring 1 Part not displayed Part A.5 Determine the total extension of the two springs Part not displayed Part A.6 Replace and Part not displayed Part A.7 Determine the extension of the equivalent system Part not displayed Hint A.8 Solving for Hint not displayed Express the effective spring constant in terms of and . ANSWER:

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## This note was uploaded on 04/07/2010 for the course PHYS 3163 taught by Professor Pickett during the Spring '10 term at CSU Long Beach.

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Ch13-periodic-motion - MasteringPhysics 10:22 PM Print View Print Introductory mechanics Chapter 13 Periodic Motion Due at 11:59pm on Tuesday

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