Law of Conservation of Linear Momentum The total momentum of a closed system is constant

1. Law of Conservation of Linear Momentum • The total momentum of a closed system is constant • (no external forces) Momentum total before=Momentum total after

2.  p = 0 Momentum Before Collision = Momentum After Collision m1v1i + m2v2i = m1v1f + m2v2f

3. 3 Types of Collisions • Elastic Collision –Momentum and kinetic Energy are conserved. • 2. Inelastic Collision – Only momentum is conserved. • 3. Perfectly inelastic collision – Only momentum is conserved and • the objects stick together after the collision. LINK

4. Below 3 bullets with equal mass run into 3 blocks of wood with equal mass.  • The first bullet passes through the block and maintains much of its original momentum, very little momentum gets transferred to the block • The second bullet, expands as it enters the block of wood which prevents it from passing all the way through it, most of its momentum gets transferred to the block.  (This is a totally inelastic collision.) • The third bullet (a rubber bullet) bounces off the block transferring all of it's own momentum and then borrowing some more from the block.  This has the most momentum transferred to the block. (This is an elastic collision.)

5. Elastic Collision The animation portrays the elastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown.

6. Elastic Collision The animation portrays the elastic collision between a 3000-kg truck and a 1000-kg car. The before- and after-collision velocities and momentum are shown.

7. Elastic Collision The animation portrays the elastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown.

8. Perfectly Inelastic Collision The animation portrays the inelastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown.

9. Perfectly Inelastic Collision The animation portrays the inelastic collision between a 3000-kg truck and a 1000-kg car. The before- and after-collision velocities and momentum are shown.

10. Perfectly Inelastic Collision The animation portrays a Perfectly inelastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown.

11. Perfectly Inelastic Collision – Objects stick together after collision and move off with same final velocity. ptBefore Collision = ptAfter Collision m1v1i + m2v2i = m1v1f + m2v2f m1v1i + m2(0) = (m1+m2)Vf m1v1i = (m1+m2) Vf m1 v1i / (m1+m2) = Vf

12. Perfectly Inelastic Collision A 100 kg astronaut, is moving at a speed of 9 m/s and runs into a stationary astronaut (mass = 150 kg). What is the velocity of the astronauts after the collision?

13. Solution

14. Zacho Zacho the clown, who has a mass of 60 kg and stands at rest on the ice, catches a 15-kg ball that is thrown to him at 20 m/sec. Zacho catches the ball and slides across the ice after the "collision". How fast does Zach and the ball move across the ice after the collision?

15. A 1100 kg truck is traveling at 10 m/s while carrying a crate of mass • 800 kg. Suddenly a flying saucer swoops down, removes the crate • without jostling the truck and flies away. What is the velocity of the • truck after the crate has been removed? (No clues are implied in the • animation.) The truck continues on at • 10 m/s. • 190/11 m/s • 8/11 m/s • 190/8 m/s

16. A railroad engine has four times the mass of a flatcar. If a diesel coasts at 5 km/hr into a flatcar that is initially at rest, how fast do the two coast if they couple together?

19. Before the momentum of the cart is 60 kgcm/s and the dropped brick is 0 kgcm/s; the total system momentum is 60 kgcm/s. After the momentum of the cart is 20 kgcm/s and the dropped brick is 40 kgcm/s; the total system momentum is 60 kgcm/s. Momentum of the system is conserved. The momentum lost by the loaded cart (40 kgcm/s) is gained by the dropped brick.

20. Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Marissa (m=40 kg) who is at rest. Rather than knock her over, she picks her up and continues in motion without "braking.“ Find the velocity of Granny and Marissa.

21. A 75 kg player, Dante “Rugby” Davis is moving at 2 m/s When he runs into a 100 kg player running at –1.5 m/s. Which direction will the resulting collision travel, in Dante’s direction or the other players? Find the final velocity of the players

22. Perfectly Inelastic Collision A large fish 4X the mass of the smaller fish is traveling at 5km/h. If the small fish was initially at rest calculate the velocity of the big fish after lunch.

23. Don’t mess with big fish pbig fish + plittle fish = pbig fish + plittle fish (4m kg · 5 km/hr) + (m kg· 0) = (4m kg · v) + (m kg · v) 20m kg km/hr = 5m kg · v v = 4 km/hr

24. A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Determine the velocity of the truck after the collision. They don’t stick together

25. Movies reinforce "bad" physics.  A misconception is if a person gets hit by a bullet they will fly backwards and break any window they were standing by. A realistic bullet has a mass of .04 kg and a velocity of 300 m/s, the only way the person would fly backwards is if the person had a mass of less than a 1 kg. People typically have masses from 45kg to 120kg, the movies don't follow the law of conservation of momentum.

26. If the impact were shown realistically a person on ice skates (to reduce friction) would barely move. The simulation uses a realistic bullet (0.04Kg at 300m/s) and a realistic person (65Kg) and treats the collision as completely inelastic (the bullet sticks).  Try the calculation for yourself, you'll find the person only goes 0.18m/s.

27. Explosion Type Problem! Total Momentum Before equals ZERO, nothing moving, after the individual momentums must add up to ZERO also.

28. EXPLOSION! A 100 kg cannon launches a 5 kg projectile forward at 20 m/s. What is the recoil velocity of the cannon?

30. If 50,000 kg of exhaust are expelled at 100 m/s how fast will the 50,000 kg shuttle take off at?

31. You (100kg) and your skinny friend • (50.0 kg) stand face-to-face on a • frictionless, frozen pond. You push • Off each other. You move backwards • with a speed of 5.00 m/s. • What is the total momentum of the you-and-your-friend system? • What is your momentum after you pushed off? • What is your friends speed after you pushed off?

32. omentum • A gun recoils when it is fired. The recoil is the result of action-reaction force • pairs. As the gases from the gunpowder explosion expand, the gun pushes • the bullet forwards and the bullet pushes the gun backwards. The • acceleration of the recoiling gun is ... • greater than the acceleration of the bullet. • smaller than the acceleration of the bullet. • the same size as the acceleration of the bullet.

33. A skater stuck on a frozen (frictionless) lake wants to get off of safely. How can she do this with no outside help? She can take her skate off and throw it. She then slides off in the opposite direction (Conservation of Momentum) This is the principle by which rockets work. Frozen Lake pt before = pt after m1v1i+m2v2i = m1vif+m2v2f 0 = 60(vs ) + 1(10) vs = -1/6 m/s