Ch.6.2 Conservation of Momentum.ppt.pptx

energy transformation

1. Ch.6.2 Conservation of Momentum

2. Warm Up An 1800 kg car with a certain velocity runs into a parked vehicle (which is free to roll). Will the velocity of the hit vehicle be faster, slower, or the same if the vehicle is: A motorcycle with 850 kg of mass? A car with equal mass? A semi truck with 9600 kg of mass?

3. When two objects collide, impulse is equal and opposite for the two objects. Before collision Impact After collision IMPULSE IMPULSE Each object has equal and opposite change in momentum. Impulse-Momentum in a Collision

4. BEFORE AFTER Momentum of object 1 = 4 kg·m/s Momentum of object 2 = 0 → Total momentum = 4 kg·m/s Momentum of object 1 = 0 Momentum of object 2 = 4 kg·m/s → Total momentum = 4 kg·m/s Since change of momentum in a collision is equal and opposite, the momentum gained by one object is the amount lost by the other. Impulse-Momentum in a Collision

5. Momentum Object 1 Before Collision Momentum Object 2 Before Collision + A B Momentum Object 1 After Collision Momentum Object 2 After Collision = + A B Conservation of Momentum [video] Law of Conservation of Momentum: the total momentum of all objects interacting with each other remains constant

6. Conservation of Momentum This is true in all collisions, no matter how many moving pieces there are! m car v car m c v c ∑ m coin v coin = m car v car m c v c m c v c m c v c

7. Construct the Equation! e.g. Conservation of Energy: ME i = ME f Formula: ½mv i 2 + mgh i = ½mv f 2 + mgh f

8. Construct the Equation! Conservation of Momentum: ∑ p i = ∑ p f Formula: ? Conservation of Momentum m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f Momentum Object 1 Before Collision Momentum Object 2 Before Collision + A B Momentum Object 1 After Collision Momentum Object 2 After Collision = + A B

9. Scenario: Complete Transfer of Momentum m 1 v 1,i m 2 v 2,i m 1 v 1,f m 2 v 2,f

10. Examples: Complete Transfer of Momentum

11. Scenario: Objects at Rest Pushing Off Each Other m 1 v 1,i + m 2 v 2,i m 1 v 1,f + m 2 v 2,f Which object will have a higher final velocity? What will the signs of the velocities be (+/-)?

12. Examples: Objects at Rest Pushing Off Each Other

13. Scenario: Objects Sticking to Each Other m 1 v 1,i + m 2 v 2,i (m 1 +m 2 )v f How will the velocity of the truck change once the apple has landed?

14. Examples: Objects Sticking to Each Other

15. Textbook Example pg.208 m 1 = 76 kg m 2 = 45 kg v 1,i = 0 v 2,i = 0 v 1,f = 2.5 m/s to the right v 2,f = ? 0 = (76 kg)(2.5 m/s) + (45 kg)v 2,f D U F A S v 2,f = – 4.2 m/s or 4.2 m/s to the left A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f → v 2,f = – m 1 v 1,f m 2

16. Future Applications Conservation of Momentum in two dimensions Conservation of Angular Momentum

17. Homework Pg.209 #1-3 HONORS: #4 So excited!