Aim: How can we apply conservation of momentum to collisions?

1. Aim: How can we apply conservation of momentum to collisions? • Identify conservation laws that you know.

2. Conservation of Momentum • In a system, the momentum of the individual components may change, but the total momentum of the system remains constant. • Law of Conservation of Momentum: • pbefore = pafter (in reference table) • How is this useful?

3. Identifying terms After Collision Before Collision 1 2 1 2

4. Car Accident • A 1,000-kg car moving at 5 m/s collides into a 1200-kg car at rest. After the collision the 1000 kg car comes to rest. • Calculate the velocity of the 1200kg car after the collision. • Calculate the total momentum before and after the collision.

5. Solution momentum before = momentum after pbefore = pafter

7. A 1,000 kg car is moving to the right at 12 m/s. Another 1500kg car is moving to the left. The cars collide and are brought to rest. Determine the initial speed of the 1500 kg car.

8. A 0.005 kg bullet is moving to the right at 200 m/s. The bullet strikes a stationary block of wood on a frictionless, level surface. The mass of the wood block is 7.0 kg. The bullet travels right through the wood and continues out the other side with a speed of 150 m/s. • 1. Calculate the speed of the block after the collision. • 2. What is the direction of the block after the collision?

9. A 0.26-kg cue ball moving at 1.2 m/s strikes a stationary 0.17-kg 8 ball. After the collision the cue ball comes to rest. • A) Calculate the magnitude of the velocity of the 8 ball after the collision. • B) Determine the total momentum after the collision.

10. A 1.0-kg ball traveling north at 3.0 m/s collides with a 4.0-kg ball at rest. Determine the magnitude of the total momentum after the collision.

11. Summary • Describe the conservation of momentum. • Identify the formula for conservation of momentum. • A 5-kg bowling ball rolling at 3m/s collides into a 6.2-kg ball at rest. After the collision the 5-kg ball comes to rest. • A) Calculate the speed of the 6.2-kg ball after the collision. • B) If the time of impact is .23 seconds, determine the force exerted on the 6.2-kg ball.

12. Aim: How can we calculate final velocity after a collision? • A 2-kg object moving at 5 m/s collides with a 4-kg object at rest. After the collision the 2-kg object comes to rest. • A) Calculate the velocity of the 4-kg object after the collision. • B) If the time of impact was .01 seconds then what is the force exerted on the 4kg object? • Is the force exerted on the 2-kg object the same? Why?

13. A 5.0-kilogram steel block is at rest. A 1.5-kilogram lump of clay is propelled at 5.0m/s at the steel block. After the collision the clay sticks to the steel block. Calculate the speed after the collision. (hint: sketch a picture)

14. Bullet and Block • A 0.1-kilogram bullet is fired horizontally with a velocity of 400m/s into a 14.6-kg wooden block at rest. The bullet is imbedded in the wooden block. Determine the speed of the block after impact.

15. A 2.0-kg object is moving at 3m/s to the right and a 4.0-kg object is moving at 8m/s to the left on a horizontal frictionless table. If the two objects collide and stick together after the collision then what is the final total momentum?

16. Summary: • 1) How can we describe an inelastic collision? • 2) Explain what happens to the masses after the collision.

17. Aim: How can we apply conservation of momentum to the recoil/explosion problem? • A 0.1-kilogram bullet is fired horizontally at 350m/s into a 5-kg wooden block at rest. The bullet is imbedded in the wooden block. Determine the speed of the block after impact. • http://www.youtube.com/watch?v=x71pa_YWgbQ

19. A hunting rifle fires a bullet of mass 0.00953 kg with a velocity of 500 m/s tothe right. The rifle has a mass of 4 kg.Calculate the recoil speed of the rifle as the bullet leaves the rifle.

20. A 62.1-kg male ice skater is facing a 42.8-kg female ice skater. They are at rest on the ice. They push off each other and move in opposite directions. The female skater moves backwards with a speed of 3.11 m/s. Determine the speed of the male skater.

21. A rock is hammered into two pieces. A 0.25-kg piece flies to the left at 5 m/s, while the other 0.5 kg piece flies to the right. How fast does the second piece fly?

22. Summary • Describe the total momentum before the explosion/recoil. • Identify the formula for recoil/explosion formula. • Explain conservation of momentum.

23. Aim: How can we apply conservation of momentum to head on collisions?

24. How can we describe the types of head on collisions? • Inelastic • Elastic

25. A 900kg car traveling west at 20 m/s collides head on with a 1,000kg car traveling east. Immediately after the collisions the cars come to rest. • Determine the initial speed of the 1,000kg car.

26. A 850kg car traveling north at 15 m/s collides with a 2,000kg car traveling south. After the collision the 850kg car rolls south at 4 m/s. The 2,000kg car come to rest. • Determine the initial speed of the 2,000kg car.

27. A 2,000kg truck traveling at 30m/s east collides with a 10,000kg bus traveling west. The vehicles lock at move together at 7 meters per second west. • Calculate the initial speed of the bus.

28. Summary: • How do we determine if the collision is inelastic or elastic? • Describe the total momentum before and after a collision.

29. Aim: How can we apply conservation of momentum to applications? • A 300 kg motorcycle moving at 15m/s east collides with a 900 kg car at rest. After the collision the 900kg car moves at 6m/s east and the 300 kg motorcycle rolls west. • A) Determine the final speed of the motorcycle. • B) If the time of impact was 0.85 seconds then calculate the force. • C) Calculate the impulse.