Linear Momentum & Impulse

1. Take out tables. On a separate sheet:Make a list of every equation we’ve already used in this class that has the velocity term in it.

2. Here is your choice: a. I toss a 25-kg bowling ball to you. b. I shoot a 1-kg cannonball at you.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. 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.

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

12. Increased force & contact time on object give greatest Dp = mDv.

13. The more time in contact, the less force needed to change p.

14. Impulse (J) is the momentum change. It has the same units. kg m or Ns s The quantity FDt (or Ft) is called impulse (J).

15. 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?

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

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

18. Non-Constant ForceForce vs. time graph. The area under the curve = impulse or Dp change in momentum.

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

20. 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?

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

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

23. 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?

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

25. 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

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

27. http://www.youtube.com/watch?v=yUpiV2I_IRI Do Now page 232 #14.

28. Consv Momentum Demos.

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

30. 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.

31. One Ball transfers all its momentum.

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

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

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

35. Recoil From Explosions

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

37. 1. 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.

38. 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

39. Recoil Hewitt 6:25 https://www.youtube.com/watch?v=1-s8NZ8xKW0

40. 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?

41. Bg fish sm.fish Bg fish sm.fish m1v1 + m2v2 = m1fv1f + m2fv2f (4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2 But the final velocities are equal so factor out the vf: 20 kg m/s = vf (4+1kg) vf = (20 kg m/s) / (5kg) = 4m/s

42. Fish lunch Hewitt 4:00 https://www.youtube.com/watch?v=MK0B5hEU7OI

43. Find the final velocity of the cart and brick together 2. A 2 kg brick is dropped on a 3 kg cart moving at 5.0 m/s.

44. cart brick cart brickm1v1 + m2v2 = m1fv1f + m2fv2f(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2150 kg m/s = v (3kg + 2 kg) (150 kg m/s )/5 kg = 3.0 m/s

45. Elastic & Inelastic Collisions Totally Elastic: no KE lost at all (to heat, light, sound etc.) Usu. Involves objects that don’t make contact. Totally Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.

46. Which is totally elastic? Inelastic?

47. Inelastic Collisionmc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0pc = pt =

48. m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000)v + (3000)v (20000 kg m/s) = (1000kg + 3000kg)v (20000 kg m/s) = (4000 kg)v (20000 kg m/s) = v4000 kg v = 5 m/s

49. Elastic Collision mc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0 Find final velocity of the car if truck has final velocity of 10 m/s.

50. m1v1 + m2v2 = m1fv1f + m2fv2f(1000kg)(20m/s) + 0 = (1000kg)vc+(3000kg)(10m/s) 20,000 kg m/s = (1000kg)vc+30000 kg m/s 20,000 kg m/s – 30,000 kg m/s = vc (1000kg) - 10 m/s = vc