C6-college physics-shyppt课件

1、2010 autumnLecture7Lecture7Linear Momentum & Linear Momentum & CollisionsCollisionsCollege physics 2010Key wordsl(linear) momentum 动量limpulse 冲量limpulse-momentum theorem 动量定理ltime-average force 平均冲力linteraction 相互作用lair bags 气囊lparticles system: composed of some particles 质点系linternal forces

2、: among particles 内力lexternal forces: acted on from surroundings 外力College physics 2010MomentumlFrom Newtons laws: force must be present to change an objects velocity (speed and/or direction)lWish to consider effects of collisions and corresponding change in velocitylMethod to describe is to use con

3、cept of linear momentumscalarvectorGolf ball initially at rest, so some of the KE of club transferred to provide motion of golf ball and its change in velocityCollege physics 2010MomentumlVector quantity, the direction of the momentum is the same as the velocityslApplies to two-dimensional motion as

4、 wellyyxxmvpandmvpvmp Size of momentum: depends upon mass depends upon velocity College physics 2010ImpulselIn order to change the momentum of an object (say, golf ball), a force must be appliedlThe time rate of change of momentum of an object is equal to the net force acting on itpGives an alternat

5、ive statement of Newtons second lawp(F*t) is defined as the impulsepImpulse is a vector quantity, the direction is the same as the direction of the forcetFporamtvvmtpFnetifnet:)(College physics 2010ConcepTestSuppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momen

6、tum, and you exert the same force to stop each. How do the time intervals to stop them compare?1. It takes less time to stop the ping-pong ball.2. Both take the same time.3. It takes more time to stop the ping-pong ball.College physics 2010ConcepTestSuppose a ping-pong ball and a bowling ball are ro

7、lling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?1. It takes less time to stop the ping-pong ball.2. Both take the same time.3. It takes more time to stop the ping-pong ball. Note: Because force equals the time r

8、ate of change of momentum, the two balls loose momentum at the same rate. If both balls initially had the same momenta, it takes the same amount of time to stop them.College physics 2010Problem: Teeing OffA 50-g golf ball at rest is hit by “Big Bertha” club with 500-g mass. After the collision, golf

9、 leaves with velocity of 50 m/s.Find impulse imparted to balla) Assuming club in contact with ball for 0.5 ms, find average force acting on golf ball.College physics 2010Problem: teeing offGiven:mass: m=50 g = 0.050 kgvelocity: v=50 m/sFind: impulse=?Faverage=?1. Use impulse-momentum relation:2. Hav

10、ing found impulse, find the average force from the definition of impulse:smkgsmkgmvmvpimpulseif50. 2050050. 0NssmkgtpFthustFp331000. 5105 . 050. 2, Note: according to Newtons 3rd law, that is also a reaction force to club hitting the ball:iiffififRVMvmVMvmorVMVMvmvmortFtF,of clubCONSERVATION OF MOME

11、NTUMCollege physics 2010Conservation of MomentumlDefinition: an isolated system is the one that has no external forces acting on itpA collision may be the result of physical contact between two objectsp“Contact” may also arise from the electrostatic interactions of the electrons in the surface atoms

12、 of the bodiesCollege physics 2010Conservation of Momentum The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system before the collision is equal to the total momentum of the syst

13、em after the collisionCollege physics 2010Conservation of MomentumlMathematically:pMomentum is conserved for the system of objectspThe system includes all the objects interacting with each otherpAssumes only internal forces are acting during the collisionpCan be generalized to any number of objectsf

14、fiivmvmvmvm22112211College physics 2010Problem: Teeing Off (cont.)Lets go back to our golf ball and club problem:smkgsmkgvvsmkgvvmsmvmsmkgpifif55 . 050. 2so,50. 2:Club50gramm50,50. 2:Ballfactor of 10 times smallerCollege physics 2010ConcepTestSuppose a person jumps on the surface of Earth. The Earth

15、1. will not move at all2. will recoil in the opposite direction with tiny velocity3. might recoil, but there is not enough information provided to see if that could happenedCollege physics 2010ConcepTestSuppose a person jumps on the surface of Earth. The Earth1. will not move at all2. will recoil in

16、 the opposite direction with tiny velocity3. might recoil, but there is not enough information provided to see if that could happened Note: momentum is conserved. Lets estimate Earths velocity after a jump by a 80-kg person. Suppose that initial speed of the jump is 4 m/s, then:smkgsmkgVsmkgVMpsmkgp

17、EarthEarthEarth2324103.5106320so,320:Earth320:Persontiny negligible velocity, in opposite directionCollege physics 2010Types of CollisionslMomentum is conserved in any collisionwhat about kinetic energy?lInelastic collisionspKinetic energy is not conservednSome of the kinetic energy is converted int

18、o other types of energy such as heat, sound, work to permanently deform an objectpPerfectly inelastic collisions occur when the objects stick togethernNot all of the KE is necessarily lostenergylostfiKEKECollege physics 2010Perfectly Inelastic Collisions:lWhen two objects stick together after the co

19、llision, they have undergone a perfectly inelastic collisionlSuppose, for example, v2i=0. Conservation of momentum becomesfiivmmvmvm)(212211.20105 . 2105,)2500(0)50)(1000(:1500,1000ifE.g.,3421smkgsmkgvvkgsmkgkgmkgmfffivmmvm)(02111College physics 2010Perfectly Inelastic Collisions:What amount of KE l

20、ost during collision?JsmkgvmvmKEiibefore622222111025. 1)50)(1000(212121JsmkgvmmKEfafter622211050. 0)20)(2500(21)(21JKElost61075. 0lost in heat/”gluing”/sound/College physics 2010More Types of CollisionslElastic collisionspboth momentum and kinetic energy are conservedlActual collisionspMost collisio

21、ns fall between elastic and perfectly inelastic collisionsCollege physics 2010More About Elastic CollisionslBoth momentum and kinetic energy are conservedlTypically have two unknownslSolve the equations simultaneously2222112222112211221121212121ffiiffiivmvmvmvmvmvmvmvmCollege physics 2010Problem Sol

22、ving for One -Dimensional CollisionslSet up a coordinate axis and define the velocities with respect to this axispIt is convenient to make your axis coincide with one of the initial velocitieslIn your sketch, draw all the velocity vectors with labels including all the given informationCollege physic

23、s 2010Sketches for Collision ProblemslDraw “before” and “after” sketcheslLabel each object pinclude the direction of velocitypkeep track of subscriptsCollege physics 2010Sketches for Perfectly Inelastic CollisionslThe objects stick togetherlInclude all the velocity directionslThe “after” collision c

24、ombines the massesCollege physics 2010Problem Solving for One-Dimensional Collisions, cont.lWrite the expressions for the momentum of each object before and after the collisionpRemember to include the appropriate signslWrite an expression for the total momentum before and after the collisionpRemembe

25、r the momentum of the system is what is conservedCollege physics 2010Problem Solving for One-Dimensional Collisions, finallIf the collision is inelastic, solve the momentum equation for the unknownpRemember, KE is not conservedlIf the collision is elastic, you can use the KE equation to solve for tw

26、o unknownsCollege physics 2010Glancing CollisionslFor a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conservedpUse subscripts for identifying the object, initial and final, and c

27、omponentsfyfyiyiyfxfxixixvmvmvmvmandvmvmvmvm2211221122112211College physics 2010Glancing CollisionslThe “after” velocities have x and y componentslMomentum is conserved in the x direction and in the y directionlApply separately to each directionCollege physics 2010Problem Solving for Two-Dimensional

28、 CollisionslSet up coordinate axes and define your velocities with respect to these axespIt is convenient to choose the x axis to coincide with one of the initial velocitieslIn your sketch, draw and label all the velocities and include all the given informationCollege physics 2010Problem Solving for

29、 Two-Dimensional Collisions, contlWrite expressions for the x and y components of the momentum of each object before and after the collisionlWrite expressions for the total momentum before and after the collision in the x-directionpRepeat for the y-directionCollege physics 2010Problem Solving for Tw

30、o-Dimensional Collisions, finallSolve for the unknown quantitiespIf the collision is inelastic, additional information is probably requiredpIf the collision is perfectly inelastic, the final velocities of the two objects is the samepIf the collision is elastic, use the KE equations to help solve for

31、 the unknownsCollege physics 2010College physics 2010Rocket propulsionlThe operation of a rocket depends upon the law of conservation of linear momentum as applied to a system of particles, where the system is the rocket plus its ejected fuel. Because the gases are given momentum when they are eject

32、ed out of the engine, the rocket receives a compensating momentum in the opposite direction. Therefore, the rocket is accelerated as a result of the “push,” or thrust, from the exhaust gases.College physics 2010Rocket PropulsionlThe rocket is accelerated as a result of the thrust of the exhaust gase

33、slThis represents the inverse of an inelastic collisionpMomentum is conservedpKinetic Energy is increased (at the expense of the stored energy of the rocket fuel)College physics 2010Rocket PropulsionlThe operation of a rocket depends on the law of conservation of momentum as applied to a system, where the system is the rocket plus its ejected