Explosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation before and after an

Transcription

1 Chapte 9. Impulse and Momentum Explosions and collisions obey some supisingly simple laws that make poblem solving easie when compaing the situation befoe and afte an inteaction. Chapte Goal: To intoduce the ideas of impulse and momentum and to lean a new poblem-solving stategy based on consevation laws.

2 Chapte 9. Impulse and Topics: Momentum Momentum and Impulse Solving Impulse and Momentum Poblems Consevation of Momentum Inelastic Collisions Explosions Momentum in Two Dimensions

3 Momentum A 10 m/s B Afte the collision A v B u What is the velocity of ball A afte the collision? ball B? What is conseved duing the collision? MOMENTUM p = mv The total momentum is the sum of momentum of ball A and momentum of ball B. 3

4 Momentum p = mv The total momentum of the system is conseved duing the collision: m v = m v + m u A A, i A B A 10 m/s B A v B u Momentum is a vecto. It has the same diection as coesponding velocity. Geneal expession fo the momentum consevation: the total momentum befoe the collision is equal to the total momentum afte the collision 4

5 Momentum Geneal expession fo the momentum consevation: the total momentum befoe the collision is equal to the total momentum afte the collision A v A, i A v A, f p = mv B v B, i B v B, f m v + m v = m v + m v A A, i B B, i A A, f B B, f Usually this equation is witten in tems of components. 5

6 Example: A 10 m/s B ma = 1kg m = 4kg B Afte the collision the balls ae moving togethe (have the same velocity). What is thei velocity? A B v Momentum befoe the collision: p = m v, = 10 i A A i kg m s Momentum afte the collision: p = ( m + m ) v = 5v f A B Consevation of momentum: pi = p f 10 = 5v v = 2 m / s 6

7 Why do we have consevation of total momentum? Newton s second law: Acceleation: Then Fnet = ma dv a = dt dv d( mv ) dp F net = m = = dt dt dt momentum Afte integation t2 = = p = F dt t 1 t 1 net t2 J F dt = net F ( t) The aea unde cuve. net It is called IMPULSE, J. The impulse of the foce is equal to the change of the momentum of the object. p = J 7

8 p i = mv ix p f = mv < fx 0 J = p p < x f i 0 8

9 m v m v = F dt 1 fx,1 1 ix,1 x,2on1 t1 t t 2 = m v m v = F dt = 2 fx,2 2 ix,2 x,1on2 t 2 1 Newton s thid law: F = F x,1 on 2 x,2 on 1 t t Then 2 2 F dt = F dt x,1on2 x,2on1 t 1 1 t ( ) m v m v = m v m v 2 fx,2 2 ix,2 1 fx,1 1 ix,1 9

10 ( ) m v m v = m v m v 2 fx,2 2 ix,2 1 fx,1 1 ix,1 m v + m v = m v + m v 1 ix,1 2 ix,2 1 fx,1 2 fx,2 p + p = p + p ix,1 ix,2 fx,1 fx,2 p = p ix, total fx, total The law of consevation of momentum 10

11 Momentum p = mv The law of consevation of momentum: The total momentum of an isolated system (no extenal foces) does not change. Inteactions within system do not change the system s total momentum A v A, i v isolated system A v A, f v B v B, i m v + m v = m v + m v B v B, f A A, i B B, i A A, f B B, f 11

12 Momentum p = mv The ball is dopped onto a had floo: The ball is not an isolated system (inteaction with the floo) no consevation of momentum fo the ball Initial momentum is Final momentum (afte collision) is p i = mv i p f = mv The ball+ the floo is an isolated system The total momentum (ball+floo) is conseved v f f v i 12

13 Example: Find v 2 x Motion with constant acceleation: ( v ) = 2a x = x, B x 1 v1 x, B = 4 m / s Isolated system Momentum befoe the collision : kg m pi, total = mbv1 x, B + mcv1 x, C = mbv1 x, B = 75 4 = 300 s Momentum afte the collision : p = m v + m v = ( m + m ) v = 100v f, total B 2 x, B C 2 x, C B C 2x 2x Consevation of momentum: p = p f, total i, total 100v = 300 v2 x = 3 m / s 2 x 13

14 Pefectly inelastic collision: A collision in which the two objects stick togethe and move with a common final velocity. p = m v + m v i, total 1 ix,1 2 ix,2 p = ( m + m ) v f, total 1 2 m v + m v = ( m + m ) v 1 ix,1 2 ix,2 1 2 fx fx m 1 m1 3 3 vix,2 = + 1 v fx vix,1 = 0.5 = 2.25 m / s m2 m

15 Chapte 9. Summay Slides

16 Geneal Pinciples

17 Geneal Pinciples

18 Impotant Concepts

19 Impotant Concepts

20 Applications

21 Applications

22 Chapte 9. Questions

23 The cat s change of momentum is A. 30 kg m/s. B. 10 kg m/s. C. 10 kg m/s. D. 20 kg m/s. E. 30 kg m/s.

24 The cat s change of momentum is A. 30 kg m/s. B. 10 kg m/s. C. 10 kg m/s. D. 20 kg m/s. E. 30 kg m/s.

25 A 10 g ubbe ball and a 10 g clay ball ae thown at a wall with equal speeds. The ubbe ball bounces, the clay ball sticks. Which ball exets a lage impulse on the wall? A. They exet equal impulses because they have equal momenta. B. The clay ball exets a lage impulse because it sticks. C. Neithe exets an impulse on the wall because the wall doesn t move. D. The ubbe ball exets a lage impulse because it bounces.

26 A 10 g ubbe ball and a 10 g clay ball ae thown at a wall with equal speeds. The ubbe ball bounces, the clay ball sticks. Which ball exets a lage impulse on the wall? A. They exet equal impulses because they have equal momenta. B. The clay ball exets a lage impulse because it sticks. C. Neithe exets an impulse on the wall because the wall doesn t move. D. The ubbe ball exets a lage impulse because it bounces.

27 Objects A and C ae made of diffeent mateials, with diffeent spinginess, but they have the same mass and ae initially at est. When ball B collides with object A, the ball ends up at est. When ball B is thown with the same speed and collides with object C, the ball ebounds to the left. Compae the velocities of A and C afte the collisions. Is v A geate than, equal to, o less than v C? A. v A > v C B. v A < v C C. v A = v C

28 Objects A and C ae made of diffeent mateials, with diffeent spinginess, but they have the same mass and ae initially at est. When ball B collides with object A, the ball ends up at est. When ball B is thown with the same speed and collides with object C, the ball ebounds to the left. Compae the velocities of A and C afte the collisions. Is v A geate than, equal to, o less than v C? A. v A > v C B. v A < v C C. v A = v C

29 The two paticles ae both moving to the ight. Paticle 1 catches up with paticle 2 and collides with it. The paticles stick togethe and continue on with velocity v f. Which of these statements is tue? A. v f = v 2. B. v f is less than v 2. C. v f is geate than v 2, but less than v 1. D. v f = v 1. E. v f is geate than v 1.

30 The two paticles ae both moving to the ight. Paticle 1 catches up with paticle 2 and collides with it. The paticles stick togethe and continue on with velocity v f. Which of these statements is tue? A. v f = v 2. B. v f is less than v 2. C. v f is geate than v 2, but less than v 1. D. v f = v 1. E. v f is geate than v 1.

31 An explosion in a igid pipe shoots out thee pieces. A 6 g piece comes out the ight end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. Fom which end does the thid piece emege? A. Right end B. Left end

32 An explosion in a igid pipe shoots out thee pieces. A 6 g piece comes out the ight end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. Fom which end does the thid piece emege? A. Right end B. Left end