1. Momentum Physics I FoxTrot: Bill Amend

2. Momentum Defined Momentum p is defined as the product of mass and velocity, mv. Units: kg m/s p = mv Momentum m = 1000 kg v = 16 m/s p = (1000 kg)(16 m/s) p = 16,000 kg m/s Author: Tippens, P. (2007)

3. IMPULSE tt F J = F  t Impulse: Impulse J is a force F acting for a small time interval  t. Author: Tippens, P. (2007)

4. Example 1: The face of a golf club exerts an average force of 4000 N for 0.002 s. What is the impulse imparted to the ball? tt F Author: Tippens, P. (2007) What is the unit for Impulse? Derive the unit from the equation. Ans: 8 Ns

5. The average force acting over an interval of time gives the same impulse as the actual force. Impulse Normally, a force acting for a short interval is not constant. It may be large initially and then play off to zero as shown in the graph. Impulse from a Varying Force

6. Impulse Changes Velocity Consider a mallet hitting a ball: F Impulse = Change in “mv” Author: Tippens, P. (2007)

7. Hailstone vs. Raindrop Which exerts a larger impulse on the car? Which exerts a larger force on the car? Explain. Hailstone

8. Impulse and Momentum Impulse = Change in momentum F  t = mv f - mv o tt F mv A force F acting on a ball for a time  t increases its momentum mv. Author: Tippens, P. (2007)

9. The Physics Classroom. [Animations].

10. Vector Nature of Momentum Consider the change in momentum of a ball that is dropped onto a rigid plate: vovo vfvf A 2-kg ball strikes the plate with a speed of 20 m/s and rebounds with a speed of 15 m/s. What is the change in momentum? + Author: Tippens, P. (2007)

11. Impluse Sample Problem An 18,000 kg bus is moving with a speed of 15 m/s. If Superman is to stop the bus in 5 seconds, what average force must he exert on the bus? Explain why Superman’s force is negative?

12. Your Turn! A 500-g baseball moves to the left at 20 m/s striking a bat. The bat applies a force of 5000 N on the ball, and it leaves in the opposite direction at 40 m/s. What was the time of contact? 40 m/s tt F 20 m/s m = 0.5 kg + - + Author: Tippens, P. (2007) Pause for Practice Ans: 0.006 sec

14. Bellringer Questions You have 2 minutes to answer the following questions. 1.Momentum is a __ quantity. A. ScalarB. vector 2. If you increase the time of impact, then you can ___ the amount of force when applying an impulse. A. IncreaseB. decreaseC. not change 3.A 2 kg mass moves right with a speed of 1 m/s and rebounds with a speed of 2 m/s. What is the change in momentum? A. 0 kg m/sB. 2 kg m/sC. 6 kg m/s

16. The diagram to the right depicts the before- and after-collision speeds of a car which undergoes a head-on-collision with a wall. In Case A, the car bounces off the wall. In Case B, the car "sticks" to the wall. 1.In which case (A or B) is the change in velocity the greatest? 2.In which case (A or B) is the change in momentum the greatest? 3.In which case (A or B) is the impulse the greatest? 4. In which case (A or B) is the force which acts upon the car the greatest (assume contact times are the same in both cases)? A A A A The Physics Classroom. [Animations].

17. Conservation of Momentum A B vAvA vB A B vAvA vBvB B The total momentum AFTER a collision is equal to the total momentum BEFORE.

18. Types of Collisions: Elastic Collision – Total Momentum and Kinetic Energy is Conserved. Objects do not stick together The Physics Classroom. [Animations].

19. Elastic Collision – Total Momentum and Kinetic Energy is Conserved. Objects do not stick together The Physics Classroom. [Animations].

20. 2. Perfectly Inelastic Collision – Only Momentum is Conserved and the objects stick together. Types of Collisions: The Physics Classroom. [Animations].

21. 1.Name the type of collision. 2.What is the momentum of the system before collision? 3.What is the final velocity of the system after collision ?

22. Momentum & Impulse - Sample Problems A 30 kg mass traveling north at 40 m/s collides head on with a 60 kg mass traveling south at 50 m/s. After the collision the 30 kg mass moves south at 50 m/s. What is the velocity of the 60 kg mass after the collision? M2M2 M1M1 V 2f ? Before After Collision

23. Your Turn! A 0.105 kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what speed does the goalie slide on the ice? 48 m/s Pause for Practice Ans: 0.067 m/s

24. Your Turn! Determine the post-collision velocity.

25. (Save for class!) A 1 kg gun fires a 5 g bullet at a speed of 180 m/s. What is the recoil velocity of the gun?

26. Save for class! A 0.112-kg billiard ball moving at 154 cm/s strikes a second billiard ball of the same mass moving in the opposite direction at 46 cm/s. The second billiard ball rebounds and travels at 72 cm/s after the head-on collision. Determine the post-collision velocity of the first billiard ball

28. Bellringer Questions You have 2 minutes to answer the following questions. Answer individually! 1.Impulse equals change in momentum. A. TrueB. False 2. A 500 kg cart is traveling at 10 m/s. What is its momentum? 3.Which leads to a greater impulse? A. A car sticking to a wall B. A car rebounding off the wall

29. Collision Videos Racquet ball Alciatore, D. High Speed Video Clips

30. Jello Drop Alciatore, D. High Speed Video Clips

31. Water balloon Alciatore, D. High Speed Video Clips

32. Soccer Ball Kick Alciatore, D. High Speed Video Clips

33. Foot Stomp Alciatore, D. High Speed Video Clips

34. Fist Bounding Alciatore, D. High Speed Video Clips

35. Rubber ball Alciatore, D. High Speed Video Clips

36. Gun Recoil Alciatore, D. High Speed Video Clips

37. Water Balloon and Pin Alciatore, D. High Speed Video Clips

38. Water Balloon Pop Alciatore, D. High Speed Video Clips

39. YouTube.com

40. Credits: Alciatore, D.(n.d.). High Speed Video Clips. Colorado State University. Retrieved with permission from http://high_speed_video.colostate.edu/http://high_speed_video.colostate.edu/ Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons. Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference Complimentary Resource CD. Tippens, P. (2007). Chapter 9A Impulse and Momentum. [PowerPoint Slides]. Received from 2007 AP Conference Complimentary Resource CD. The Physics Classroom. [Animations]. http://www.thephysicsclassroom.comhttp://www.thephysicsclassroom.com