MIT 8 01  Mechanical Energy and Simple Harmonic Oscillator (8 pages)
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Mechanical Energy and Simple Harmonic Oscillator
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Lecture Notes
 Pages:
 8
 School:
 Massachusetts Institute of Technology
 Course:
 8 01  Classical Mechanics
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Unformatted text preview:
Summary Change in Mechanical Energy G G G F total Fc total Fnc total Total force final Mechanical Energy and Simple Harmonic Oscillator Total work W total initial G G F total dr final G total F c G G Fnctotal dr initial final G G Fctotal dr Change in potential energy U total Total work done is change in kinetic energy W total U total Wnc K Mechanical Energy Change E mechanical K U total initial 8 01 Week 09D1 Conclusion Modeling the Motion using Force and Energy Concepts Force and Newton s Second Law Mechanical Energy Accounting Initial state Draw all relevant free body force diagrams Identify non conservative forces Total initial kinetic energy final Total initial potential energy initial Total initial mechanical energy G G Wnc Fnc dr Calculate non conservative work Change in Mechanical Energy Choose initial and final states and draw energy diagrams Choose zero point P for potential energy for each interaction in which potential energy difference is well defined Identify initial and final mechanical energy Apply Energy Law Wnc K U total Wnc K U total K initial K1 initial K 2 initial U initial U1 initial U 2 initial mechanical Einitial K initial U initial Final state Total final kinetic energy K final K1 final K 2 final Total final potential energy U final U1 final U 2 final Total final mechanical energy mechanical Efinal K final U final Apply Energy Law mechanical mechanical Wnc Efinal Einitial 1 Example Energy Changes A small point like object of mass m rests on top of a sphere of radius R The object is released from the top of the sphere with a negligible speed and it slowly starts to slide Find an expression for the angle with respect to the vertical at which the object just loses contact with the sphere Example Energy Changes A small point like object of mass m rests on top of a sphere of radius R The object is released from the top of the sphere with a negligible speed and it slowly starts to slide Find an expression for the angle with respect to the vertical
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