Lect07 - Fall 2011 PHYS 172 Modern Mechanics Lecture 7 –...

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Unformatted text preview: Fall 2011 PHYS 172: Modern Mechanics Lecture 7 – Speed of Sound in a Solid, Buoyancy Read 4.9 – 4.13 1 Speed of sound in solids s k m ! = Qualitatively: Larger ω , larger v Larger d , larger v Detailed derivation: v d ! = Speed of sound in a solid 2 Derivative form of the Momentum Principle The Momentum Principle ! ! p = ! F net ! t ! ! p ! t = ! F net The rate of the momentum change is equal to force Works only if force is constant during Δ t If force changes introduce instantaneous rate of change: d ! p dt ! lim " t # " ! p " t The momentum principle d ! p dt = ! F net 3 Newton’s Second Law d ! p dt = ! F net Assume nonrelativistic case : ! p = m ! v d m ! v ( ) dt = ! F net m d ! v dt = ! F net (definition of acceleration) ! F net = m ! a Newton’s second law Traditional form of 2 nd Newton’s law (Assume m = const) Newton’s original formulation : The rate of change of amount of body’s motion is proportional to force momentum Momentum principle is the second Newton’s law 4 Spring-mass system: horizontal...
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Lect07 - Fall 2011 PHYS 172 Modern Mechanics Lecture 7 –...

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