Partial Solns Manual - Andy Ruina

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40 Chapter 10.1. Dynamics of a particle in space Problem 10.1.22 (continued)Introduction to Statics and Dynamics, c Andy Ruina and Rudra Pratap 1992-2009.
Chapter 10.1. Dynamics of a particle in space Problem 10.1.26 4110.1.26 Bungy Jumping. In a relativelysafe bungy jumping system, people jumpup from the ground while being pulled upby a rope that runs over a pulley at O andis connected to a stretched spring anchoredat B. The ideal pulley has negligible size,mass, and friction. For the situation shownthe spring AB has rest length `0 D 2 m anda stiffness of k D 200 N= m. The inextensiblemassless rope from A to P has length`r D 8 m, the person has a mass of 100 kg.Take O to be the origin of an xy coordinatesystem aligned with the unit vectors O{ andO|a) Assume you are given the positionof the person * r D xO{ C y O| and thevelocity of the person v D PxO{ CPy O|. Find her acceleration in termsof some or all of her position, hervelocity, and the other parametersgiven. Then use the numbers given,where supplied, in your final answer.ĵOb) Given that bungy jumper’s initialposition and velocity are * r 0 D1 mO{ 5 m O| and v 0 D 0 write computercommands to find her positionat t D p = 2 s.c) Find the answer to part (b) withpencil and paper (that is, find ananalytic solution to the differentialequations, a final numerical answeris desired).Filename:s97p1-3îAPm10 mkBg = 10 m/s 2ground, no contactafter jump offProblem 10.26: Conceptual setup for abungy jumping system.Introduction to Statics and Dynamics, c Andy Ruina and Rudra Pratap 1992-2009.
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Page 3 and 4: 9.1.15 Consider a force F .t/ actin
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100 Chapter 13.4. 2D rigid-object a
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14.1.1 A disk of radius R is hinged
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112 Chapter 14.1. Rigid object kine
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114 Chapter 14.2. Dynamics of a rig
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120 Chapter 14.3. Kinematics of rol
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126 Chapter 14.4. Mechanics of cont
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15.1.5 Picking apart the polar coor
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138 Chapter 15.1. Polar coordinates
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140 Chapter 15.1. Polar coordinates
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142 Chapter 15.3. General expressio
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156 Chapter 15.4. Kinematics of 2-D
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Partial Solns Manual - Andy Ruina

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