Linear Momentum & Impulse

1. Take out tables. On a separate sheet:Make a list of every equation we’ve not yet used in this class.

2. Here is your choice: a. I toss a bullet at you. b. I shoot a bullet at you from a gun.Which is more dangerous to you?Why?

3. Linear Momentum&Impulse

4. Linear Momentum = mass in motion A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

5. Momentum (p) depends on: mass & velocity of object. p = mvm in kg v in m/s Units are … kg m no name. s

6. Momentum is aVector Quantity Same direction as velocity All Energy KE too is a scalar

7. Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum? p = mv = (2250 kg)(25 m/s) = 5.6 x 104kg m s

8. Change in momentum - accloccurs any time an object changes velocity (speed or direction).

9. Momentum Change &Newton’s 2nd Law • F = ma • F = m(Dv/Dt) • FDt =mDv m (vf - vi) for const mass. • FDt = Dp Impulse. • Dp = Change in momentum

10. Stand up • Try to hit a home run. • Try to drive a golf ball really far.

11. Equations of Momentum Change • J =FDt = Dp Impulse = change momentum. • pf – pi. • Dp = mvf – mvi • for velocity change with constant mass can factor out mass you can write, • m (vf - vi) or mDv.

12. Force is required to change velocity or momentum of a body in motion.Force must be in contact for some time.

13. Increased force & contact time on object give greatest impulseDp = mDv.

14. Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse D p.

15. Impulse (J) is the momentum change. It has the same units. kg m or Ns s It is like force but includes a contact time component!

16. Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?

17. F = 100 NDv = 50 m/sm = 50 kg Ft = mDv t = mDv F 50 kg(50 m/s) 100 kg m/s2 = 25 s.

18. Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.

19. Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.

20. Examples of Impulse/Change in Momentum • Baseball batter swinging through ball. • Applying brakes of car over time to stop.

21. Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?

22. Ft = mDv t = mDv FF = 250 Nm= 100 kgDv =190 m/st = 100kg(190m/s) 250 kg m/s2. = 76 s.

23. Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car? 2400 - N

24. Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s:a) what was its Dv?b) What was its Dp?

25. Dv = vf – vi.-12 m/s – (15 m/s) = - 27 m/s. Dp = mDv = 0.4kg(27m/s) =10.8 kg m/s

26. How many water balloons does it take to stop a bullet? 3:30 • http://www.unwindly.com/i/772-How-Many-Water-Balloons-Does-It-Take-To-Stop-A-Bullet

27. Running with momentum. 15 min. • https://www.youtube.com/watch?v=jLIyDfkQcsk • Relaxing with impulse.13 minutes. • https://www.youtube.com/watch?v=0nOHLThv2mw

28. Understanding Car Crashes 22 minstart 8:53 • Hewitt Momentum 4:20 • https://www.youtube.com/watch?v=2FwhjUuzUDg http://www.youtube.com/watch?v=yUpiV2I_IRI

29. Hwk read text 208 – 211do pg 214 #1- 4 conceptsdo p 211 #1 - 4. Impulse prbs.Also worksheet “Impulse Momentum”

30. Which are units of Impulse? Nm N/s Ns N/m A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is: 1.5 kgm/s 1.8 kgm/s 2.4 kgm/s 4.8 kgm/s

31. A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball? 0.36 kgm/s 0.72 kgm/s 1.1 kgm/s 1.8 kgm/s

32. Graphs

33. Constant force f - t graph:Dp /Impulse is area under curve FDt. Force N

34. Non-Constant ForceForce vs. time graph. The area under the curve = impulse or Dp change in momentum. What is the impulse during the 9 seconds of contact? 225 Ns

35. Consv Momentum Demos.

36. Conservation of Momentum If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.

37. What is a system? Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s). Common examples: collisions, explosions.

38. One Ball transfers all its momentum.

39. The astronaut transfers part of his momentum to the second astronaut.

40. Conservation of Momentum Calc’s • Total momentum before = total after interactions. • Collisions. • Explosions • Pushing apart.

41. To Calculate: SPbefore = Spafterm1v1 + m2v2 = m1fv1f + m2fv2f v1 and v2 velocities for objects one and two. m1 andm2 masses of objects

42. Recoil From Explosions

43. Recoil illustrates conservation of momentum where initial and final momentum = 0.0 = p1 + p2.

44. 1. Two spring loaded lab carts A and B, explode apart from rest. Cart A is twice the mass of cart B. The final velocity of cart A is 2 m/s. What is the final momentum of the system? • 0

45. 2. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon. - 5 m/s = vcf

46. Before Firing After Firingm1v1 + m2v2 = m1fv1f + m2fv2f0 = (100kg)vcf + (5kg)(100m/s) -500 kgm/s = (100 kg) vcf - 5 m/s = vcf recoil velocity of cannon

47. 3. A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank? • 1.9 m/s

48. Hwk. Consv Momentum wksht

49. Collisions • Sticky • Bouncy

50. Stick em together problems Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final velocity?