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Chapter 9. Impulse and Momentum - Physics & …

Chapter 9. Impulse and Chapter 9. Impulse and MomentumMomentumExplosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation beforeand afteran beforeand afteran Goal:To introduce the ideas of Impulse and Momentum and to learn a new problem-solving strategy based on conservation : Momentum and Impulse Solving Impulse and Momentum Problems Conservation of Momentum Chapter 9. Impulse and Chapter 9. Impulse and Momentum Momentum Conservation of Momentum Inelastic Collisions Explosions Momentum in Two Dimensions Momentum AB10 m/sAfter the collision ABvu3 What is the velocity of ball A after the collision? ball B?What is conserved during the collision?

Chapter 9. Impulse and Momentum Explosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation before and after an interaction. Chapter Goal: To introduce the ideas of impulse and ... 4 • Momentum is a vector. It has the same direction as corresponding ...

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Transcription of Chapter 9. Impulse and Momentum - Physics & …

1 Chapter 9. Impulse and Chapter 9. Impulse and MomentumMomentumExplosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation beforeand afteran beforeand afteran Goal:To introduce the ideas of Impulse and Momentum and to learn a new problem-solving strategy based on conservation : Momentum and Impulse Solving Impulse and Momentum Problems Conservation of Momentum Chapter 9. Impulse and Chapter 9. Impulse and Momentum Momentum Conservation of Momentum Inelastic Collisions Explosions Momentum in Two Dimensions Momentum AB10 m/sAfter the collision ABvu3 What is the velocity of ball A after the collision? ball B?What is conserved during the collision?

2 MOMENTUMThe total Momentum is the sum of Momentum of ball A andmomentum of ball B. p mv====rrrrrrrrMomentum The total Momentum of the system is conserved during the collision:AB10 m/sABvup mv====rrrrrrrr,A A iABm vm v m u=+=+=+=+4vu Momentum is a vector. It has the same direction as corresponding velocity. General expression for the Momentum conservation: the total Momentum before the collision is equal to the total Momentum after the collisionMomentum ABAp mv====rrrrrrrr General expression for the Momentum conservation: the total Momentum before the collision is equal to the total Momentum after the collision,A ivrrrr,B ivrrrr,A fvrrrrvrrrr5B,,,,A A iB B iA A fB B fm vm vm vm v+=++=++=++=+rrrrrrrrrrrrrrrr,B fvrrrrUsually this equation is written in terms of components.

3 Example: AB10 m/sAfter the collision the balls are moving together (have the same velocity). What is their velocity? AB1 Amkg====4 Bmkg====6 ABv,10iA A ikg mpm vs ======== Momentum before the collision: Momentum after the collision:()5fABpmm vv=+==+==+==+=Conservation of Momentum :ifpp====105v====2 /vm s====Newton s second law:momentumnetFma====rrrrrrrrWhy do we have conservation of total Momentum ? Acceleration:dvadt====rrrrrrrrThen()netd vd mvdpFmdtdtdt============rrrrrrrrrrrrrrrr 7 The area under is called Impulse , J. netFmdtdtdt============21tnettpF dt = = = = rrrrrrrrAfter integration( )netFtrrrr21tnettJF dt==== r rr rr rr rThe Impulse of the force is equal to the change of the Momentum of the object.

4 P J = = = =rrrrrrrriixpmv====0ffxpmv=<=<=<=<80xfiJ pp= <= <= <= <211,11,1,21tfxixx ontm vm vFdt = = = = 212,22,2,12tfxixx ontm vm vFdt = = = = Newton s third law:,12,21x onx onFF= = = = 9,12,21x onx onFF= = = = Then2211,12,21ttx onx onttFdtFdt= = = = (((())))2,22,21,11,1fxixfxixm vm vm vm v = = = = (((())))2,22,21,11,1fxixfxixm vm vm vm v = = = = 1,12,21,12,2ixixfxfxm vm vm vm v+=++=++=++=+,1,2,1,2ixixfxfxpppp+=++=++ =++=+10,1,2,1,2ixixfxfxpppp+=++=++=++=+, ,ix totalfx totalpp====The law of conservation of momentumMomentum AAp mv====rrrrrrrr,A ivrrrrvrrrrThe law of conservation of Momentum : The total Momentum of an isolated system (no external forces) does not within system do not change the system s total momentumisolated system11BB,,,,A A iB B iA A fB B fm vm vm vm v+=++=++=++=+rrrrrrrrrrrrrrrr,A iv,B ivrrrr,A fv,B fvrrrrMomentum p mv====rrrrrrrrThe ball is dropped onto a hard floor: The ball is not an isolated system (interaction with the floor) no conservation of Momentum for the ball Initial Momentum is Final Momentum (after collision) isiipmv====rrrrrrrrffpmv====rrrrrrrr12iv rrrrfvrrrr The ball+ the floor is an isolated system The total Momentum (ball+floor) is conservedExample: Find2xvIsolated system13 Motion with constant acceleration.

5 21 ,1()216x Bxva x========1 ,4 /x Bvm s====Isolated systemMomentum before the collision :,1 ,1 ,1 ,75 4300i totalBx BCx CBx Bkg mpm vm vm vs =+== ==+== ==+== ==+== = Momentum after the collision :,2 ,2 ,22()100f totalBx BCx CBCxxpm vm vmm vv=+=+==+=+==+=+==+=+=Conservation of Momentum :,,f totali totalpp====2100300xv====23 /xvm s====Perfectly inelastic collision:A collision in which the two objects stick together and move with a common final velocity.,1,12,2i totalixixpm vm v=+=+=+=+14,12()f totalfxpmm v=+=+=+=+1,12,212()ixixfxm vm vmm v+=++=++=++=+11,2, /22ixfxixmmvvvm smm =+ = = =+ = = =+ = = =+ = = Chapter 9.

6 Summary SlidesChapter 9. Summary SlidesGeneral PrinciplesGeneral PrinciplesImportant ConceptsImportant ConceptsApplicationsApplicationsChapter 9. QuestionsChapter 9. QuestionsThe cart s change of Momentum isA. 30 kg 10 kg 10 kg 20 kg 30 kg cart s change of Momentum isA. 30 kg 10 kg 10 kg 20 kg 30 kg They exert equal impulses because they have equal 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds. The rubber ball bounces, the clay ball sticks. Which ball exerts a larger Impulse on the wall?have equal The clay ball exerts a larger Impulse because it Neither exerts an Impulse on the wall because the wall doesn t The rubber ball exerts a larger Impulse because it They exert equal impulses because they have equal 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds.

7 The rubber ball bounces, the clay ball sticks. Which ball exerts a larger Impulse on the wall?have equal The clay ball exerts a larger Impulse because it Neither exerts an Impulse on the wall because the wall doesn t The rubber ball exerts a larger Impulse because it A and C are made of different materials, with different springiness, but they have the same mass and are initially at rest. When ball B collides with object A, the ball ends up at rest. When ball B is thrown with the same speed and collides with object C, the ball rebounds to the left. Compare the velocities of A and C after the collisions. Is vAgreater than, equal to, or less than vC? > < vCObjects A and C are made of different materials, with different springiness, but they have the same mass and are initially at rest.

8 When ball B collides with object A, the ball ends up at rest. When ball B is thrown with the same speed and collides with object C, the ball rebounds to the left. Compare the velocities of A and C after the collisions. Is vAgreater than, equal to, or less than vC? > < vCThe two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it. The particles stick together and continue on with velocity vf. Which of these statements is true? v2. less than greater than v2, but less thanv1. v1. greater than v1. The two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it. The particles stick together and continue on with velocity vf.

9 Which of these statements is true? v2. less than greater than v2, but less v1. greater than v1. An explosion in a rigid pipe shoots out three pieces. A 6 g piece comes out the right end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. From which end does the third piece emerge?piece emerge?A. Right endB. Left endAn explosion in a rigid pipe shoots out three pieces. A 6 g piece comes out the right end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. From which end does the third piece emerge?piece emerge?A. Right endB. Left


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