Momentum in Collisions and Explosions: Examples and Problem Solving

1. Lecture 12:Collisions and Explosions • Momentum Examples! • Problem Solving • Collisions (elastic & inelastic) • Explosions

2. Impulse and Momentum:quick review • Momentum-Impulse Theorem • FtI = pf- pi=p • For single object…. • If F = 0, then momentum conserved (p = 0) • For “system” of objects … • ptotal  p • Internal forces: forces between objects in system • External forces: all other forces • Fextt=ptotal • if Fext = 0 , then total momentum conserved (ptotal = 0) • Applications: Collisions & Explosions

3. “before” m2 m1 “after” m2 m1 “before” M “after” m2 m1 Collisions Procedure • Draw “before”, “after” • Define system so that Fext = 0 • Set up axes • Compute Ptotal “before” • Compute Ptotal “after” • Set them equal to each other Explosions

4. Some Terminology • Elastic Collisions: collisions that conserve mechanical energy • Inelastic Collisions: collisions that do not conserve mechanical energy • Completely Inelastic Collisions: objects stick together

5. y x Collision Example • Two cars are approaching an intersection. The first car is 1520 kg and is moving east at 18 m/s; the second car is 1380 kg and is moving north at 16 m/s. The cars have a completely inelastic collision. What is their final velocity? Before: After:

6. y x Collision Example • Two cars are approaching an intersection. The first car is 1520 kg and is moving east at 18 m/s; the second car is 1380 kg and is moving north at 16 m/s. The cars have a completely inelastic collision. What is their final velocity? x-direction: pix = pfx (1520 kg)(18 m/s) + 0 = pfx y-direction: piy = pfy 0 + (1380 kg)(16 m/s) = pfy

7. y x Collision Example • Two cars are approaching an intersection. The first car is 1520 kg and is moving east at 18 m/s; the second car is 1380 kg and is moving north at 16 m/s. The cars have a completely inelastic collision. What is their final velocity? x-direction: (1520 kg)(18 m/s) + 0 = pfx (1520 kg)(18 m/s) = (1520 kg + 1380 kg) vfx y-direction: 0 + (1380 kg)(16 m/s) = pfy (1380 kg)(18 m/s) = (1520 kg + 1380 kg) vfy

8. y x Collision Example • Two cars are approaching an intersection. The first car is 1520 kg and is moving east at 18 m/s; the second car is 1380 kg and is moving north at 16 m/s. The cars have a completely inelastic collision. What is their final velocity? x-direction: vfx = 9.43 m/s y-direction: vfy = 7.61 m/s Vf = 12.1 m/s at 51º east of north

9. y x Explosion Example • A ball has a mass of 3 kg. It explodes into three equal masses, shooting a 1 kg piece in the positive y direction with speed v and another 1 kg piece in the positive x direction with speed v. What is the speed and direction of the remaining 1 kg piece? Before: After:

10. y x Explosion Example • A ball has a mass of 3 kg. It explodes into three equal masses, shooting a 1 kg piece in the positive y direction with speed v and another 1 kg piece in the positive x direction with speed v. What is the speed and direction of the remaining 1 kg piece? x-direction: pix = pfx 0 + 0 + 0 = 0 + (1 kg) v + (1 kg) vfx y-direction: piy = pfy 0 + 0 + 0 = (1 kg) v + 0 + (1 kg) vfy

11. y x Explosion Example • A ball has a mass of 3 kg. It explodes into three equal masses, shooting a 1 kg piece in the positive y direction with speed v and another 1 kg piece in the positive x direction with speed v. What is the speed and direction of the remaining 1 kg piece? x-direction: vfx = -v y-direction: vfy = -v Vf = v 2 at 45º below the –x axis

12. Center of Mass = Balance point L m m L m 5m Center of Mass Example 1: xCM = (0 + mL)/2m = L/2 Example 2: xCM = (0 + 5mL)/6m = 5L/6 X=0 X=L

13. Summary • Collisions and Explosions • Draw “before”, “after” • Define system so that Fext = 0 • Set up axes • Compute ptotal “before” • Compute ptotal “after” • Set them equal to each other • Center of Mass (Balance Point)