Lect05 - Spring 2012 PHYS 172: Modern Mechanics Lecture 5...

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Unformatted text preview: Spring 2012 PHYS 172: Modern Mechanics Lecture 5 Predicting Motion, Conservation of Momentum Read 3.5 3.15 1 Today Predicting Motion System of Many Objects onservation f omentum Conservation of Momentum Electric Force Large or Small? Can we REALLY predict The Future? 2 Predicting motion of a planet & p 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 oes not work because the force is 3 & F 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. 3 Iterative Prediction of Motion & p Simple case: One Star (fixed in space) + One Planet 1. Calculate gravitational force: & F grav on2by1 = - G m 2 m 1 & r 2- 1 2 r 2- 1 2. Update momentum & p f = & p i + & F net t hoose hort enough & F 3. Calculate v and update position Choose t short enough ( F & v do not change much) & r f = & r i + & v avg t 4. Repeat Critical parameter: t 4 Iterative Prediction of Motion 5 Constant Force (mg) + Momentum Principle = Projectile Motion (curved path) But, can also add air resistance = non-constant force 5 Iterative prediction of motion Real case: many objects objects are free to move 1. Calculate net force on each mass: & F on m i = & F m j on m i i j 2. Update momentum of each mass & & & 3. Calculate v and update position of each mass p f = p i + F net t Choose t short enough ( F & v do not change much)...
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Lect05 - Spring 2012 PHYS 172: Modern Mechanics Lecture 5...

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