Mike attaches a 3.00 kg lead ball to a string to make a pendulum of length 10.0 meters. Let us call the position at which the lead ball hangs down vertically and is at rest the equilibrium position. Mike then pulls the lead ball to the side so that its center is raised to a vertical height of 0.0409 meters above its equilibrium position, and he gives the lead ball (pendulum bob) a push. Thus Mike gives the pendulum bob an initial kinetic energy of 2.00 J as he releases it. Assume there is no air resistance or friction. Choose the reference level for potential energy at the bottom of the pendulum's swing (the equilibrium position). a) What is the total initial energy of the pendulum as Mike releases it? b)  What is the instantaneous speed of the pendulum bob at the lowest point of its swing? c) When the lead ball (pendulum bob) is at the lowest point of its swing, the kinetic energy of the pendulum?

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.52P: A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where...
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Mike attaches a 3.00 kg lead ball to a string to make a pendulum of length 10.0 meters. Let us call the position at which the lead ball hangs down vertically and is at rest the equilibrium position. Mike then pulls the lead ball to the side so that its center is raised to a vertical height of 0.0409 meters above its equilibrium position, and he gives the lead ball (pendulum bob) a push. Thus Mike gives the pendulum bob an initial kinetic energy of 2.00 J as he releases it. Assume there is no air resistance or friction. Choose the reference level for potential energy at the bottom of the pendulum's swing (the equilibrium position). a) What is the total initial energy of the pendulum as Mike releases it? b)  What is the instantaneous speed of the pendulum bob at the lowest point of its swing? c) When the lead ball (pendulum bob) is at the lowest point of its swing, the kinetic energy of the pendulum? 

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