Conservation of Momentum Continued S2:A8: 12/09/08

Transcription

1 Conservation of Momentum Continued S2:A8: 12/09/08

2 Do Now: Get out your note books We are still working on Note Book RHP #81 Topic Conservation of Momentum, Date: 12/08/08 & 12/09/08 Copy onto RHP of your notebook Objective SWBAT apply the Law of the Conservation of Momentum.

3 Agenda Do Now Lecture on Conservation of Momentum Classwork on Conservation of Momentum Conservation of Momentum Review

4 Today s Lecture Conservation of Momentum

5 Conservation of Momentum The total momentum of a system remains constant. A system is collection of objects.

6 Applying Conservation of Momentum Conservation of Momentum can be applied to the following interactions between objects: Collisions: objects collide with each other. Separations: objects are pushed away from each other.

7 Types of collisions Sticky Collision the objects collide and become attached after the collision. Two train cars collide and remain joined together after the collision. Non-sticky Collision the objects collide and separate. A bat hits a baseball.

8 Conservation of Momentum Formula Conservation of momentum requires that: Momentum Before = Momentum After p Before = p After For a system with two objects: m 1 v 1 Before + m 2 v 2 Before = m 1 v 1 After + m 2 v 2 After

9 Sticky Collision Example A railroad car of 2000 kg coasting at 3.0 m/s collides and locks together with a second 2000 kg railroad car which is at rest. What is the velocity of the two cars after the collision? m1v1 Before + m2v2 Before = m1v1 After + m2v2 After For a sticky collision this becomes: m1v1 Before + m2v2 Before = ( m1+ m2) v After 2000kg 3m/s kg 0m/s = ( 2000kg kg) v 6000 kg m/s + 0 = (4000 kg ) v 6000 kg m/s = (4000 kg ) v 6000 kg m/s = v 4000 kg v = 1.5 m/s

10 PTG #1 (page S101) A railroad car of 2000 kg coasting at 3.0 m/s overtakes and locks together with a identical car coasting on the same track in the same direction at 2.0 m/s. What is the speed of the two cars after they lock together? m1v1 Before + m2v2 Before = m1v1 After + m2v2 After For a sticky collision this becomes: m1v1 Before + m2v2 Before = ( m1+ m2) v After 2000 kg 3 m/s kg 2 m/s = ( 2000kg kg) v 6000 kg m/s kg m/s = (4000 kg ) v 10,000 kg m/s = (4000 kg ) v 10,000 kg m/s = v 4000 kg v = 2.5 m/s

11 PTG #2 (page S101) In a hockey game, an 80 kg player skating at 10.0 m/s overtakes and bumps from behind a 100 kg player who is moving in the same direction at 8.0 m/s. As a result of being bumped from behind, 100 kg player s speed increases to 9.78 m/s. What is the 80 kg player s speed after the bump? m1v1 Before + m2v2 Before = m1v1 After + m2v2 After 80 kg 10 m/s kg 8 m/s = 80 kg v kg 9.78 m/s 800 kg m/s kg m/s = 80 kg v kg m/s 1,600 kg m/s = 80 kg v kg m/s 1,600 kg m/s kg m/s = 80 kg v1 622 kg m/s = 80 kg v1 622 kg m/s = v1 80 kg v1 = m/s

12 PTG #4 (page S101) A 45 kg female figure skater and her 75 kg male skating partner begin their ice dancing performance standing at rest in face-to-face position with the palms of their hands touching. Cued by the dance music, both skaters push-off with their hands to move in backward. If the female skater moves at 2 m/s relative to the ice, what is the velocity of the male skater? (Hint: The momentum before the skaters push off is zero.) m1v1 Before + m2v2 Before = m1v1 After + m2v2 After For a push-off starting at rest m1v1 Before + m2v2 Before = m1v1 After + m2v2 After = m1v1 After + m2v2 After 0 = m1v1 After + m2v2 After 0 = 45 kg 2m/s + 75 kg v2 0 = 90 kg m/s + 75 kg v2-90 kg m/s = 75 kg v2-90 kg m/s = v2

13 MCAS QUESTION #7 Overview Lets review the problem statement and set up a demo. Is this a collision or a separation? (A) It is a collision so the conservation of momentum applies. Is it a sticky collision or a non-sticky collision? (A) It is a sticky collision because the objects stay joined together.

14 MCAS QUESTION #7 Problem Analysis What is the significance of the frictionless surface? (A) cart will remain at a constant speed per Newton s 1 st Law. What is the significance of the block dropping straight down? (A) block does not affect the motion of the cart in the horizontal direction.

15 MCAS QUESTION #7 Answers The cart will move to the left at a velocity less than the original velocity of the cart. The cart will move to the left at a velocity greater than the original velocity of the cart. The cart will move to the right at a velocity less than the original velocity of the cart. The cart will move to the right at a velocity greater than the original velocity of the cart.

16 MCAS QUESTION #25 Calculate the momentum of both marbles before the collision. Calculate the momentum of both marbles after the collision. If the velocity of the red marble doubles, how will the velocity of the yellow marble change after the collision? If the red marble had more mass than the yellow marble, how would the momentum of the yellow marble change after the collision?

17 N.U.Separations: Now You Try It! a. Two children on ice skates start at rest and push off from each other. One has a mass of 30 kg and moves back at 2 m/sec. The other has a mass of 15 kg. What is the second child s speed? Answer: 4 m/sec b. Standing on an icy pond, you throw a 0.5 kg ball at 40 m/sec. You move back at 0.4 m/sec. What is your mass? Answer: 50 kg

18 N.U. Now You Try It! An astronaut floating in space throws a 2- kilogram hammer to the left at 15 m/sec. If the astronaut s mass is 60 kilograms, how fast does the astronaut move to the right after throwing the hammer