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1 Momentum & Kinetic Energy Mr. Finn 2011-2012

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Slide 2 Any motion? M V M V Oh, dear! Al vectorsscalars Should motion be described using vectors or scalars?

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Slide 3 Momentum DefinitionDefinition –quantity of motion –inertia velocity or VectorVector –scalar vector = vector –same direction as velocity UnitsUnits –no special name: kg m/s Why use “p”?? German: der Impuls (for momentum) Why use “p”?? German: der Impuls (for momentum)

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Slide 4 Why both KE and Momentum? Both depend on mass and velocity... two... So why do we need two different quantities when KE = p 2 /2m?

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Slide 5 When two objects interact...... they affect each other’s motion,... but something about the motion remains constant... while something else changes changes. Momentum is constant. Energy changes form.

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Slide 6 Tackling Awesome Alex stopping Awesome Alex weighs 200 lb and runs 8 ft/s. Speedy Gonzales weighs only 100 lb but runs 16 ft/s, while Ponderous Poncho runs only 4 ft/s but weighs 400 lb. In the encounter, who will be more effective in stopping Alex? (a) Speedy Gonzales (b) Ponderous Poncho (c) Both the same Epstein (1997): 93 Something remains constant!

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Slide 7 “Hurting” Awesome Alex hurt Awesome Alex weighs 200 lb and runs 8 ft/s. Speedy Gonzales weighs only 100 lb but runs 16 ft/s, while Ponderous Poncho runs only 4 ft/s but weighs 400 lb. In the encounter, who will hurt poor Alex more when tackling him? (a) Speedy Gonzales (b) Ponderous Poncho (c) Both the same Epstein (1997): 93 Something changes!

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Slide 8 Two Different Quantities These situations show that E = same is quite different from P = same –KE = “ability to damage something” internal change (structure) –P = “ability to stop something” external change (motion) KE and P measure different aspects of motion –energy changes form, momentum does not! Now, consider examples of these differences...

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Slide 9 In a classroom demonstration, an anvil shields a daring (if foolish) physics professor from most of the sledgehammer’s: (a) momentum. (b) kinetic energy. (c) both. (d) neither (that’s why he’s foolish!) Daring Physics Professor Epstein (1997): 96-98 Energy converts to heat, sound, … but momentum is not!

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Slide 10 Run, Jenny! Run! momentumkinetic energy Jenny starts to run from rest. She puts a certain amount of momentum and kinetic energy into herself and how much into the ground? (a) more (b) less (c) the same amount as into herself. Note: there are TWO separate questions! Epstein (1997): 71

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Slide 11 Work & Impulse Impulse: I = F t = P –always equal & opposite forces equal & opposite due to N3L timeequaltime of application equal for both objects: A pushes on B for the same time B pushes back on A Work: F x = KE –NOT equal & opposite forces equal & opposite due to N3L displacementsunequaldisplacements are unequal - depending on amount of inertia m – x = 1/2 a ( t) 2 = 1/2 (F/m) ( t) 2 P always equal and opposite but one object can gain more KE than another loses - but HOW??

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Slide 12 Energy vs. Momentum Energy changes form –PE KE heat –work is the conversion of energy from one form to another neverMomentum never changes form or direction –p x separately conserved from p y or momentum in x-direction is not converted into momentum in another direction (y) –p never converts to heat/thermal energy Jenny is burning calories from her food!

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Slide 13 Impulse = change in P m M Same impulse = Ft same momentum gained m M Moves farther more work done more KE gained Lighter object gains more KE

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Slide 14 Work = change in KE m M Same work = Fd same KE gained More time to move greater impulse applied more momentum gained Massive object gains more P M d m d

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Slide 15 Newton’s Cradle Pull two balls back and two balls pops out the other side. Why not just one? Pull one ball back and one pops out the other side. Why not two? Hewitt 8 th ed (1998): 116

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Slide 16 Rolling in the Rain momentumspeedkinetic energy An open car rolls in a vertically- falling downpour. The momentum, speed, and kinetic energy of the car will: (a) increase (b) decrease (c) not change Note: there are THREE separate questions! Epstein (1997): 87-88 Friction turns KE to heat

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Slide 17 Rolling Drain The rain stopped. A drain plug is pulled and the water runs out. speedmomentumkinetic energy The speed, momentum, and kinetic energy of the car will: (a) increase (b) decrease (c) not change Note: there are THREE separate questions! Epstein (1997): 89

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Slide 18 What happens when objects slide & stop? motion Where does motion come from? potential energy kinetic energy no momentum forward & backward momentum kinetic energy What happens to the kinetic energy? mechanical energy heat via friction friction = non-conservative force momentum What happens to the momentum? transferred to the Earth as momentum via friction friction = external force

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Slide 19 René Descartes (1596 - 1650) The total momentum in the Universe remains constant.

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Slide 20 Why Is Momentum Conserved? Recall: or No restriction on type of force –friction does not dissipate momentum No external force, rate of change of is zero –closed, isolated system Based on Newton’s Laws –Newton’s 3rd Law = equal & opposite exchange of momentum Whenever momentum changes, we say a force acted, or the object interacted with something else via a force. Universe Universe N3L: F A B = - F B A F A B t = - F B A t P B = - P A N3L: F A B = - F B A F A B t = - F B A t P B = - P A

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Slide 21 Why is Energy Conserved? Work: W = KE + PE + … Energy more general concept than forces/Newton Laws of Motion –Energy changes form to chemical, radiant, … Indirect consequence of Newton’s 2 nd Law –Need to expand into thermodynamics, … total... for conservation of total energy N3L: F A B = - F B A F A B x B - F B A x A KE B - KE A N2L: W = KE + PE + … N3L: F A B = - F B A F A B x B - F B A x A KE B - KE A N2L: W = KE + PE + …

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Slide 22 James Joule (1818-1889) Energy (the capacity for work) can only be converted into various external forms, and it cannot be created from nothing or destroyed (Robert Mayer, 1842; James Prescott Joule, 1843; Hermann von Helmholtz, 1847)Robert Mayer

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Slide 23 One More Question (a) standing where they were initially. (b) standing farther away from each other. (c) standing closer together. (d) moving away from each other. (e) moving toward each other. Two people on frictionless roller blades throw a ball back and forth. After a couple of throws, they are: Mazur (1997): 136

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Slide 24 In Summary Momentum: –vector quantity –always conserved, never converted Energy: –scalar quantity –always conserved, but changes form Momentum Momentum is what stays constant. Energy Energy is what allows changes.

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Slide 25 Conservation of Energy –time symmetry = scalar only one temporal dimension time = ordering events for cause/effect Conservation of Momentum –spatial symmetry = vector momentum conserved in each direction space = arrangement of events Why need both P and KE? Emmy Noether

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Slide 26 Why Bother???? Newton’s Laws = classical physics –Interactions = forces –Changes = acceleration Conservation Laws = modern physics –Interactions = exchange of particles (bosons) carry energy & momentum –Changes = quantum states uncertainty principle Newton EinsteinBohr Energy and Momentum bridge the gap between the classical physics of Newton and the modern physics of Einstein & Bohr.

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Slide 27 Robert Mayer (1814-1878)

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Slide 28 Christiaan Huygens (1629-1695) First to develop idea of “kinetic energy” –did not like “momentum” cancels out even if objects moving want measure of motion not depending on direction –mv 2 is “conserved” under proper conditions Leibniz, Young –linked to work/energy G.G. Coriolis –“kinetic energy” = 1/2 mv 2 –defined work W = F ∆x vis viva = “living” force

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