2. Presentation designed by DBHS physics department Momentum Inertia in Motion

3. Presentation designed by DBHS physics department Definition of Momentum Momentum is the product of mass and velocity. Momentum Mass Velocity

4. Presentation designed by DBHS physics department Momentum Depends on Velocity An object must be moving in order to have momentum. Consider the truck at rest. Consider the skate boarder. He has momentum.

5. Presentation designed by DBHS physics department Momentum Depends on Mass Larger objects traveling at the same velocity as smaller objects will have greater momentum.

6. Presentation designed by DBHS physics department The Nature of Momentum Momentum is a vector quantity. –It has magnitude (how big). –It has direction (right(+) or left(-)). Direction is denoted by sign (+ or -). 235

7. Presentation designed by DBHS physics department Calculating Momentum As mentioned before, momentum is the product of mass and velocity.

8. Presentation designed by DBHS physics department Practice Problem 1 Calculate the momentum of the tank if its velocity is to the right.

9. Presentation designed by DBHS physics department Practice Problem 2 Calculate the momentum of the tank if its velocity is to the left.

10. Presentation designed by DBHS physics department Collisions The collisions that we will study will involve two objects. Each object possesses its own momentum. Collisions are broken down into two categories: –Elastic (Objects Separate) –Inelastic (Objects Stick Together)

11. Presentation designed by DBHS physics department Momentum – Elastic Collisions Elastic Collision – a collision in which the colliding bodies do not stick together. The equation used for elastic collisions is as follows.

12. Presentation designed by DBHS physics department Momentum – Inelastic Collisions Inelastic Collision – a collision in which the colliding bodies stick together. The equation used for elastic collisions is as follows.

13. Presentation designed by DBHS physics department Elastic Collisions The total momentum of the system remains constant. Elastic collision, objects move off with separate velocities. This means that they can bounce. Or they can be projected from rest (like a cannon).

14. Presentation designed by DBHS physics department Momentum Identify the number and types of collisions in the animation below.

15. Presentation designed by DBHS physics department Momentum Identify the number and types of collisions in the animation below.

16. Presentation designed by DBHS physics department The Law of Conservation of Momentum In a closed and isolated system, the total momentum of all the objects present remains constant.

17. Presentation designed by DBHS physics department Elastic Collision Equation BeforeAfter Subsripts: I: Initial (Before) F: Final (After) Initial Momentum Object 1 Initial Momentum Object 2 Final Momentum Object 1 Final Momentum Object 2

18. Presentation designed by DBHS physics department Sample Problem (Elastic) What is the initial momentum of the blue ball? Before 1.0kg 2.0kg v 1I = 8.0m/sv 2I = -3.0m/s What is the initial momentum of the red ball? After 1.0kg 2.0kg v 1F = -6.0m/s v 2F = ? What is the final momentum of the blue ball? What is the final momentum of the red ball? What is the final velocity of the red ball?

19. Presentation designed by DBHS physics department Practice Problem 3 (Elastic) Two air track cars collide and bounce. The red car is initially traveling at a velocity of 0.50m/s to the right while the yellow car is traveling at a velocity of 1.5m/s to the left. After the collision the red car is moving 2.0m/s to the left with the yellow car following, but not touching. Air Track 0.3kg0.8kg m red = 0.3kg m yellow = 0.8kg What is the initial momentum of the red car?What is the initial momentum of the yellow car? What is the final momentum of the red car? What is the final momentum of the yellow car? What is the final velocity of the yellow car? Collide

20. Presentation designed by DBHS physics department Sample Problem (Elastic) This problem will demonstrate the “cannon type” scenario. –The cannon and cannonball are initially at rest. –The ball then is fired at a velocity of 150m/s. m cannon = 300kg m ball = 10kg What is the initial momentum of the cannon? What is the initial momentum of the cannonball?What is the final momentum of the cannonball?What is the momentum of the cannon immediately after firing? What is the velocity of the cannon immediately after firing? Fire!

21. Presentation designed by DBHS physics department Practice Problem 4 (Elastic) A gun (m = 1.5kg), initially at rest, is fired sending its bullet (m = 0.1kg) at a velocity of. Before After What is the initial momentum of the gun and bullet? What is the total momentum of the system before firing? What is the total momentum of the system after firing? What is the final momentum of the bullet? What is the final momentum of the gun? What is the final velocity of the gun?

22. Presentation designed by DBHS physics department Inelastic Collisions The Law of Conservation of Momentum: that the total momentum of the system remains constant, no matter what the collision. In an inelastic collision, objects stick together. This means that they have the same final velocity (v F ). N S S N v1v1 v2v2 vFvF vFvF Collide

23. Presentation designed by DBHS physics department Inelastic Collision Equation The inelastic collision equation takes into account the momentum of each object before and after the collision. Because the objects are combined after the collision, and they have the same final velocity (v F ).

24. Presentation designed by DBHS physics department BeforeAfter Inelastic Collision Equation Initial Momentum Object 1 Initial Momentum Object 2 Final Combined Momentum Objects 1 & 2

25. Presentation designed by DBHS physics department Sample Problem (Inelastic) The big rig backs up with an initial velocity of 2.0m/s and collides with the trailer, which is initially at rest. What is the initial momentum of the truck? What is the initial momentum of the trailer? What is the combined mass of the truck and trailer?What is the final velocity of the truck and trailer combo? m Truck = 2000.0kg m Trailer = 3000.0kg BeforeAfter

26. Presentation designed by DBHS physics department ICE Practice Problem 5 (Inelastic) Happy Penguin (m = 7.0kg) slides across the ice on a magnet with a velocity of 3.0m/s. Cool Penguin (m = 8.0kg) comes up from behind with a velocity of 5.0m/s. He, also having a magnet, will collide and stick. S N C N S H S N C N S H What is the initial momentum of Cool Penguin?What is the final momentum of Happy Penguin?What is the combined mass of the two penguins?What is the final velocity of the penguin pair? Collide

27. Presentation designed by DBHS physics department Momentum  While climbing a cliff, a super model (m = 51.0 kg) slips and falls.  She falls for 2s before she is rescued by Super Doctor Physics (m = 63.0 kg, v = 27.85 m/s).  What was their velocity immediately after the collision?

28. Presentation designed by DBHS physics department Impulse (  mv) When objects collide, their velocities change. This means that their individual momentums will also change. Impulse simply defines the change in momentum for an individual object (denoted by  mv).

29. Presentation designed by DBHS physics department Impulse (  mv) There are two ways to calculate impulse: –You can subtract initial momentum from final momentum. –Or you can take the product of force and time. The units for impulse are in Ns, which is equal to kgm/s

30. Presentation designed by DBHS physics department Sample Problem 1 (Impulse) A golf ball, initially at rest, is struck by a golf club. –The golf ball (m = 0.1kg) rolls away with a velocity of 35m/s. What is the initial momentum of the ball?What is the final momentum of the ball?What is the impulse on the ball? Swing

31. Presentation designed by DBHS physics department Practice Problem 6 (Impulse) A soccer ball (m = 0.4kg) approaches a player with a velocity of 13m/s (left). The player kicks the ball giving it a new velocity of 20m/s (right). What is the initial momentum of the soccer ball?What is the final momentum of the soccer ball?What is the impulse felt by the soccer ball? Kick

32. Presentation designed by DBHS physics department Sample Problem 2 (Impulse) A baseball is struck by a bat with a force of 3000N for a duration of 0.05s. What is the change in momentum of the baseball? or Hit

33. Presentation designed by DBHS physics department Practice Problem 7 (Impulse) A tennis ball is struck with a force of 400N for a time of 0.15s. What is the impulse felt by the tennis ball? Hit

34. Presentation designed by DBHS physics department Summary All problems surrounding momentum are based on the following principles: –Momentum depends on both mass and velocity. –Momentum is conserved, regardless of collision. –Collision type determines the equation used. –Impulse is simply change in momentum. Trains are stupid cuz they can’t do Physics!