Momentum-Impulse Relationship

1. Momentum-Impulse Relationship Review

2. What is momentum? • “Mass in Motion” • What is impulse? • The quantity “force x time interval” • Change in momentum • The amount of force and the amount of time it takes to change the momentum • Definition of Impulse • I=Ft • Definition of Momentum • P=mv • The impulse-momentum relationship • Ft=Δmv

3. Increasing Momentum • If you want to produce the maximum increase in momentum of something • Apply the greatest force • Extend the time of application • Example: The follow through with your swing in baseball • Giving a stalled car a sustained push instead of a brief one

4. Decreasing Momentum Over a Long Time • If you are out of control in a car, would you rather hit a brick wall or a haystack? • A haystack right? • Why? • Which has a greater impulse? • They have the same impulse. Why? • Because the result in both is a momentum of “0” • However, stopping is a product, it doesn’t mean that the time or force was the same

5. Haystack vs. Wall • By hitting the haystack instead of the wall, you • Extend the time of impact • The time it takes you to change your momentum to zero Ft mV

6. mV Ft

7. Decreasing Momentum over a Short Time • For short impact times, the impact forces are large! • Remember: for an object brought to rest, the impulse is the same no matter how it is stopped. But, if the time is short, the force will be large

8. Conservation of Momentum

9. Law of Conservation of Motion • In the absence of an external force, the momentum of a system remains unchanged. • Whenever a system remains unchanged , we call that conserved. • We say momentum is conserved.

10. Example • Consider a gun being fired. • A gun recoils when it is fired. • The recoil is the result of action-reaction force pairs. • Newton’s 3rd Law • As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. • What is the recoil momentum of the gun? • The same as the momentum of the gases and bullet it fires!

11. Why? • The momentum gained by the bullet is equal and opposite to the momentum gained by the recoiling gun. • They cancel each other out • No momentum is gained, and no momentum is lost. Momentum is conserved.

12. Practice Problems

13. A 340 kg. garbage can hits a wall at 5 m/s. What is the momentum at impact?

14. A 3.4 kg. garbage can lid hits a wall at 5 m/s. What is the momentum at impact?

15. If the object in the first problemmoved through the wall in 2 seconds, what is the force of the impulse?

16. A bullet is fired from a gun at 760 m/s and it has a mass of 0.1 kg, and it has a time of impact of 3 s. The bulletproof glass that it strikes can withstand a force of 23 N. Will the bullet break through the glass?

17. Collisions Momentum Conserved

18. Collisions Net momentum before collision = net momentum after collision Two types of collisions Elastic Collision: A collision in which colliding objects rebound completely. Momentum is transferred from one object to another Inelastic Collision: A collision in which the colliding objects stick together resulting in the coupling of colliding objects.

19. COLLISIONS • In any collision, we can say that • Net momentum before collision=net momentum after collision • Elastic collision • Momentum is transferred from one object to another

20. Elastic Collision Example(m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final p=(400)(2)=800kgm/s p=(500)(5)=2500kgm/s Total p = 2500+800 =3300kgm/s p=(500)(3)=1500kgm/s p=(400)(4.5)=1800kgm/s Total p= 1500+1800=3300 kgm/s

21. Example 2 (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final • In this example the car is not moving before the collision. Calculate the total momentum before the collision. ptruck + pcar • Assume that our collision results the same way our marbles moved; the truck has 0 velocity after the collision, what would the velocity of the car be? Would you expect it to be higher, lower or the same as the truck’s? Why?

22. Example 3 (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final • What happens when we change the position of the two vehicles? Calculate the total momentum. • Assume that our collision results the same way our marbles moved; the car has 0 velocity after the collision, what would the velocity of the truck be? Would you expect it to be higher, lower or the same as the car’s? Why?

23. Let’s Do an Example Together A freight car (500kg) is moving down a track at 10m/s when it collides with another parked freight car (500 kg). They do not stick together, so the second freight car gets bumped down the track. What is the final velocity of the second car? (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final Draw Picture:

24. V=10 V=0 500 kg 500 kg V=?? V =0 500 kg 500 kg

25. Solution: • Net momentum before collision = net momentum after collision • (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final • (500kg)(10m/s) + (500kg)(0m/s) = (500kg)(0m/s) +(500kg)(vfinal) • 5000kgm/s + 0 = 0 + 500kg(vfinal) • 5000kgm/s = vfinal 500kg 10m/s = vfinal

26. When two objects collide and they stick together Initialfinal m1v1 +m2v2 = (m1 + m2)v Inelastic Collisions

27. Inelastic Collision - Example Initialfinal m1v1 +m2v2 = (m1 + m2)v (80)(6)+(40)(0) = 120v 480 + 0 = 120v V= 4m/s

28. Collisions Continued Initialfinal m1v1 +m2v2 = (m1 + m2)v Find the final velocity after this collision.

29. Another Example: A freight car moving along a track at 10m/s collides with another freight car at rest. If the freight cars are of equal mass (500 kg) and stick together by the collision, what is the velocity of the coupled cars after the impact? Initialfinal m1v1 +m2v2 = (m1 + m2)v Draw Picture:

30. V=10 V=0 500 kg 500 kg V=??

31. Solution: • Net momentum before collision = net momentum after collision Initialfinal • m1v1 +m2v2 = (m1 + m2)v • (500 kg) (10 m/s) + (500 kg)( 0 m/s) = (500kg + 500kg)( v) • 5000 kg m/s = 1000 kg x v • 5000 kgm/s = 1000 kg x v 1000 kg 1000 kg V=5 m/s