# ps09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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11/4/2010 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Problem Set 9: Practice Problems Exam 2 Exam 2 will take place on Wednesday November 10 from 7:30-9:30 pm. Exam 2 Room Assignments: Section L01 Room 26-100 Room 50-340 Walker Memorial Section L02 Room 26-100 Section L03 Room 10-250 Section L04 Room 26-100 Section L05 Room 50-340 Walker Memorial Section L06 Room 10-250 Section L07 Room 50-340 Walker Memorial Conflict Exam 2 will take place on Friday November 12 from 9-11 am and 10-12 am. You need to email your instructor and get his ok if you plan to take the conflict exam. Please include your reason. Concept Questions and Analytic Problems Test Two Topics: Work, Kinetic Energy, Potential Energy, Mechanical Energy, Work-Mechanical Energy Theorem, Conservation of Energy Simple Harmonic Motion: Equation of Motion, Solution with Initial Conditions, Period and Angular Frequency, Conservation of Energy. Momentum, Impulse, Center of Mass. External Force and Change in Momentum, Conservation of Momentum, Continuous Mass Transfer Collisions: Elastic and Inelastic. Experiment 3: Conservation of Energy Practice problems: The following problems are only for practice and should not be handed in.

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11/4/2010 2 Problem 1: Simple Pendulum by Energy Method Solution A simple pendulum consists of a massless string of length l and a point like object of mass m is attached to one end. Suppose the string is fixed at the other end and is initially pulled out at an angle of 0 ! from the vertical and released at rest. a. Use the fact that the energy is constant to find a differential equation describing how the second derivative of the angle the object makes with the vertical varies in time. b. Find an expression for the angular velocity of the object at the bottom of its swing. c. Now assume that the initial angle 0 1 rad << and thus use the small angle approximation sin " to show that the simple pendulum behaves like a simple harmonic oscillator. d. Also use the approximation 2 0 0 cos 1 2 " # , to find an expression for the angular velocity of the object at the bottom of its swing.
11/4/2010 3 Problem 2 An air column of cross sectional area A and height h contains a diatomic gas. The gas pressure P is sufficiently high to support a piston of mass m . When the piston is displaced from the equilibrium position by distance ( ) y t , the internal pressure changes and there is a restoring force whose y-component is given by 0 ( ) ( ) y A P F t y t h ! = " , where 1.4 " for diatomic gases and 0 P is the equilibrium gas pressure. You may ignore gravity. a) Find the differential equation for ( ) y t . b)

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## This note was uploaded on 04/13/2011 for the course PHYSICS 8.01 taught by Professor Guth during the Fall '09 term at MIT.

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ps09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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