Lect05

# Lect05 - PHYS 172 Modern Mechanics Lecture 5 Predicting...

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Fall 2011 PHYS 172: Modern Mechanics Lecture 5 – Predicting Motion, Conservation of Momentum Read 3.5 – 3.15 1

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EXAM 1 • WHEN: Wednesday, Sept. 14, 8-10 PM • Where: Elliott Hall of Music • Material through 4.3 of text and homework: CH04-HW01 . • A practice exam with solutions will be posted in the Exams folder. 2 This is a 1 hour exam but you will be allowed 2 hours to complete it.
Today •Predicting Motion •System of Many Objects •Conservation of Momentum •Electric Force – Large or Small? •Can we REALLY predict The Future? 3

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4 Predicting motion of a planet ! p ! F Where will the planet be after one month? ! r f = ! r i + ! v avg ! t Use position update formula: If we assume that velocity is constant Does not work because the force is changing the velocity! The direction of force on planet changes with position. The momentum changes with position. In general, there is no algebraic equation to predict the motion of more than 2 interacting objects. 4
Iterative Prediction of Motion ! p ! F Simple case: One Star (fixed in space) + One Planet 1. Calculate gravitational force: 3. Calculate v and update position ! F grav on2by1 = ! G m 2 m 1 ! r 2 ! 1 2 ˆ r 2 ! 1 2. Update momentum ! p f = ! p i + ! F net ! t Choose Δ t short enough ( F & v do not change much) ! r f = ! r i + ! v avg ! t 4. Repeat Critical parameter: Δ t 5

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6 Iterative Prediction of Motion Constant Force (mg) + Momentum Principle = Projectile Motion (curved path) But, can also add air resistance = non-constant force 6
Iterative prediction of motion Real case: many objects objects are free to move 1. Calculate net force on each mass: 3. Calculate v and update position of each mass !

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## This note was uploaded on 12/07/2011 for the course PHYS 172 taught by Professor ? during the Fall '08 term at Purdue.

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Lect05 - PHYS 172 Modern Mechanics Lecture 5 Predicting...

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