1. Aim: How can we apply conservation of momentum to collisions? Aim: How can we apply conservation of momentum to collisions? Identify conservation laws that you know. 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. 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: Law of Conservation of Momentum: p before = p after (in reference table) p before = p after (in reference table) How is this useful? How is this useful?

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

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. 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 velocity of the 1200kg car after the collision. Calculate the total momentum before and after the collision. Calculate the total momentum before and after the collision.

5. Solution momentum before = momentum after momentum before = momentum after p before = p after p before = p after

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. 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. 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. 1. Calculate the speed of the block after the collision. 2. What is the direction 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 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. A) Calculate the magnitude of the velocity of the 8 ball after the collision. B) Determine the total momentum 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. 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. Describe the conservation of momentum. Identify the formula for 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 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. 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. 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 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. 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? 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? 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) 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. 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? 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? 1) How can we describe an inelastic collision? 2) Explain what happens to the masses after the 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. 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 http://www.youtube.com/watch?v=x71pa_ YWgbQ http://www.youtube.com/watch?v=x71pa_ YWgbQ 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 to the right. The rifle has a mass of 4 kg. Calculate the recoil speed of the rifle as the bullet leaves the rifle. A hunting rifle fires a bullet of mass 0.00953 kg with a velocity of 500 m/s to the 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. 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? 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. Describe the total momentum before the explosion/recoil. Identify the formula for recoil/explosion formula. Identify the formula for recoil/explosion formula. Explain conservation of momentum. 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 Inelastic Elastic 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. 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. 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. 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. 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. 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. Calculate the initial speed of the bus.

28. Summary: How do we determine if the collision is inelastic or elastic? How do we determine if the collision is inelastic or elastic? Describe the total momentum before and after a collision. 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 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. A) Determine the final speed of the motorcycle. B) If the time of impact was 0.85 seconds then calculate the force. B) If the time of impact was 0.85 seconds then calculate the force. C) Calculate the impulse. C) Calculate the impulse.