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Conceptual Physics Energy Sources Collisions Conceptual Physics Energy Sources Collisions Lana Sheridan De Anza College July 13, 2017 Last time • energy and work • kinetic energy • potential energy • conservation of energy • energy transfer • simple machines • efficiency Overview • discussion of energy sources • momentum and collisions Sources of Energy Discussion! Sources of Energy Sources of energy: • oil • coal • natural gas • wood / charcoal / peat • solar - photovoltaics and heating • wind • waves • hydroelectric • geothermal • nuclear - thermonuclear, fission, and fusion(?) Sources of Energy: Fraction of US Energy supply 1US Energy Information Administration. Sources of Energy: Costs 1Wikipedia, NEA estimates. Sources of Energy: Costs 1Wikipedia, California Energy Commission estimates. Carbon Dioxide 1Graph from http://climate.nasa.gov/evidence/ Global Temperature Record 1Figure by Robert A. Rohde, using data from 11 different studies. Current Event: Larsen C Ice Sheet Breakup Just this week (confirmed yesterday) a 6,000-square-kilometer iceberg (about the size of Delaware) broke off of Antarctica. 1John Sonntag, NASA Current Event: Larsen C Ice Sheet Breakup 1NOAA, NASA CIMSS Collisions The conservation of momentum is very useful when analyzing what happens to colliding objects. In all collisions (with no external forces) momentum is conserved: net momentum before collision = net momentum after collision pnet,i = pnet,f Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. 258 Chapter 9 Linear Momentum and Collisions Because all velocities in Figure 9.7 are either to the left or the right, they can be Before the collision, the particles move separately. represented by the corresponding speeds along with algebraic signs indicating direction. We shall indicate v as positive if a particle moves to the right and nega- S S v1i v2i tive if it moves to the left. Chapter 9 Linear Momentum and Collisions 258 In a typical problem involving elastic collisions, there are two unknown quanti- Elastic Collisionsm1 m2 ties, and Equations 9.16 and 9.17 can be solved simultaneously to find them. An Because all velocities in Figure 9.7 are either to the left or the right, they can be a Before the collision, the alternative approach, however—one that involves a little mathematical manipula- particles move separately. representedtion of Equation by the 9.17—oftencorresponding simplifies speeds alongthis process. with algebraic To see how,signs letindicating us cancel the direction.1 We shall indicate v as positive if a particle moves to the right and nega- factor 2 in Equation 9.17 and rewrite it by gathering terms with subscript 1 on the S S tive if it moves to the left. After thev1i collision, thev2 i left and 2 on the right: particles continue to move In a typical problem involving elastic collisions, there are two unknown quanti- 2 2 2 2 separatelym1 with new velocities.m2 ties, and Equations 9.16 and m9.171(v 1cani 2 bev1f solved) 5 m 2simultaneously(v2f 2 v2i ) to find them. An a alternative approach, however—one that involves a little mathematical manipula- S S Factoring both sides of this equation gives v1f v2f tion of Equation 9.17—often simplifies this process. To see how, let us cancel the 1 factor 2 in Equation 9.17 and rewrite it by gathering terms with subscript 1 on the m1(v1i 2 v1f) (v1i 1 v1f) 5 m2(v2f 2 v2i)(v2f 1 v2i) (9.18) After the collision, the left and 2 on the right: b particles continue to move Next, let us separate the terms2 containing2 2 m1 and2 m2 in Equation 9.16 in a simi- separately with new velocities. m1(v1i 2 v1f ) 5 m2(v2f 2 v2i ) Figure 9.7 Schematic represen- lar way to obtain tation ofS an elastic head-onS colli- Factoring both sides of this equation gives v1f v2f sion between two particles. m1(v1i 2 v1f) 5 m2(v2f 2 v2i) (9.19) m1(v1i 2 v1f) (v1i 1 v1f) 5 m2(v2f 2 v2i)(v2f 1 v2i) (9.18) b To obtain our final result, we divide Equation 9.18 by Equation 9.19 and obtain Next, let us separate the terms containing m1 and m2 in Equation 9.16 in a simi- 1 5 1 Figure 9.7 Schematic represen- lar way to obtain v1i v1f v2f v2i tation of an elastic head-on colli- Now rearrange terms once again so as to have initial quantities on the left and final sion between two particles. m1(v1i 2 v1f) 5 m2(v2f 2 v2i) (9.19) quantities on the right: To obtain our final result, we divide Equation 9.18 by Equation 9.19 and obtain v1i 2 v2i 5 2(v1f 2 v2f) (9.20) Pitfall Prevention 9.3 v1i 1 v1f 5 v2f 1 v2i Not a General Equation Equation This equation, in combination with Equation 9.16, can be used to solve problems 9.20 can only be used in a very spe- Nowdealing rearrange with termselastic once collisions. again so This as to pair have of initial equations quantities (Eqs. on 9.16 the leftand and 9.20) final is easier cific situation, a one- dimensional, quantitiesto handle on than the right:the pair of Equations 9.16 and 9.17 because there are no quadratic elastic collision between two terms like there are in Equationv1i 2 v 9.17.2i 5 2According(v1f 2 v2f) to Equation 9.20, the relative(9.20) veloc- Pitfall Prevention 9.3 objects. The general concept is ity of the two particles before the collision, v 2 v , equals the negative of their conservationNot a General of Equation momentum Equation (and This equation, in combination with Equation 9.16,1 ican be2i used to solve problems conservation9.20 can only ofbe kinetic used in energya very spe if - dealingrelative with velocity elastic after collisions. the collision, This pair 2 (ofv1 fequations 2 v2f). (Eqs. 9.16 and 9.20) is easier thecific collision situation, is a elastic) one- dimensional, for an iso- to handleSuppose than the the masses pair of and Equations initial 9.16velocities and 9.17 of bothbecause particles there areare no known. quadratic Equations latedelastic system. collision between two terms9.16 likeand there9.20 arecan in be Equation solved for 9.17. the According final velocities to Equation in terms 9.20, ofthe the relative initial veloc velocities- objects. The general concept is ity of the two particles before the collision, v 2 v , equals the negative of their conservation of momentum (and because there are two equations and two unknowns:1i 2i relative velocity after the collision, 2(v 2 v ). conservation of kinetic energy if m 21f m 2f 2m the collision is elastic) for an iso- Suppose the masses and initial velocities1 2 of both particles2 are known. Equations v1f 5 v1i 1 v2i (9.21) lated system. 9.16 and 9.20 can be solved for them 1final1 m velocities2 inm terms1 1 m 2of the initial velocities because there are two equations and two unknowns: a 2m b am 2 m b 5 1 1 2 1 v2f m1 2 m2 v1i 2m2 v2i (9.22) v 5 m1 1 mv 2 1 m1 1vm 2 (9.21) 1f 1 1i 1 2i m1a m2 b m1 a m2 b It is important to use the appropriatea b signsa for v1i andb v2i in Equations 9.21 and 9.22. 2m1 m2 2 m1 Let us consider somev 5 special cases.v If1 m1 5 m2, Equationsv 9.21 and 9.22(9.22) show that 2f m 1 m 1i m 1 m 2i v1f 5 v2i and v2f 5 v1i , which1 means2 that the1 particles2 exchange velocities if they have equal masses. That isa approximatelyb whata one observesb in head-on billiard ball It is important to use the appropriate signs for v1i and v2i in Equations 9.21 and 9.22. collisions: the cue ball stops and the struck ball moves away from the collision with Let us consider some special cases. If m1 5 m2, Equations 9.21 and 9.22 show that v1thef 5 samev2i and velocity v2f 5 vthe1i , which cue ball means had. that the particles exchange velocities if they have If equal particle masses. 2 is Thatinitially is approximately at rest, then whatv2i 5 one 0, and observes Equations in head-on 9.21 billiardand 9.22 ball become collisions: the cue ball stops and the struck ball moves away from the collision with m1 2 m2 the same velocity the cue ball had. v 5 v (9.23) 1f m 1 m 1i Elastic collision: particle 2 If particle 2 is initially at rest, then v2i 5 0,1 and Equations2 9.21 and 9.22 become initially at rest a b m1 2 m22m v 5 1v (9.23) 1f v2f 5m 1 m 1i v1i (9.24) Elastic collision: particle 2 1 m1 12 m2 initially at rest a b 2am1 b If m1 is much greater than mv2 and5 v2i 5 0, wev see from Equations 9.23 and(9.24) 9.24 that 2f m 1 m 1i v1f < v1i and v2f < 2v1i.
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