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Lect15

# Lect15 - PHYS 172 Modern Mechanics Fall 2009 Lecture 15...

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Fall 2009 PHYS 172: Modern Mechanics Lecture 15 - Multiple Particle Systems Read 8.1 - 8.5

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Ch 1 Changes imply interactions Vectors are used to describe many changes Momentum is fundamental: p = γ m v . Ch 2 The momentum principle: Δ p = F Δ t Interactions correspond to forces . Use Δ r =( p /m) Δ t to predict future positions (position update formula) Review of What We’ve Covered Thus Far
Ch 3 Can use position update formula for variable forces too: Gravity Electric Reciprocity: These few principles were the basis for Exam 1. v F = " G Mm r 2 ˆ r r F = 1 4 "# o q 1 q 2 r 2 ˆ r r F 12 = ! r F 21 Review of What We’ve Covered Thus Far

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Ch 4 Instantaneous (derivative) momentum principle, Spring F =-k s Δ x Mass-spring model of atoms, Y=k s /d. Speed of sound v~ ω d Analytic mass-spring solution: x(t)=Acos( ω t) Normal force, Tension force Forces parallel & perpendicular to motion: e.g. Circular Motion d r p dt = r F Principles Covered by Exam 2
Work simple particle: explain nuclear fission, fusion Potential energy = -(work by internal forces) (Multiparticle K+U can be viewed as increased mass in a single-particle model of the system) " W = v F # " r r W = v F ! d r r " E = " mc 2 = mc 2 + K U G = " G m 1 m 2 r U E = 1 4 "# o q 1 q 2 r U s = 1 2 kx 2 Chapter 5: The Energy Principle Δ E sys = W ext + Q

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Δ E sys =W ext +Q Choice of system Energy accounting Dissipation, air resistance, friction… Damped Harmonic Oscillator, Driven Harmonic Oscillator Ch 7 Energy quantization
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Lect15 - PHYS 172 Modern Mechanics Fall 2009 Lecture 15...

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