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
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 = mv m in kg
v in m/s
Units are … kg m no name. s

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

7. p = mv = (2250 kg)(25 m/s) = 5.6 x 104 kg m s
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 kg m s

8. Change in momentum - accl occurs 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 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 impulse Dp = mDv.

14. Hit a homerun needs large impulse
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
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 N Dv = 50 m/s m = 50 kg
Ft = mDv
t = mDv F
50 kg(50 m/s) kg m/s2 = 25 s.

18. Concept: A pitcher throws a fastball to a catcher
 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
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. F F = 250 N m= 100 kg Dv =190 m/s t = 100kg(190m/s)
Ft = mDv t = mDv F F = 250 N m= 100 kg Dv =190 m/s t = 100kg(190m/s) 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
Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car? 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

27. Running with momentum. 15 min.
Relaxing with impulse.13 minutes.

28. Understanding Car Crashes 22 min start 8:53
Hewitt Momentum 4:20

29. Hwk read text 208 – 211 do pg 214 #1- 4 concepts do p 211 #1 - 4
Hwk read text 208 – 211 do pg 214 #1- 4 concepts do p 211 # 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 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 Force Force vs. time graph
Non-Constant Force Force 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. SPbefore = Spafter m1v1 + m2v2 = m1fv1f + m2fv2f
To Calculate:
SPbefore = Spafter m1v1 + m2v2 = m1fv1f + m2fv2f
v1 and v2 velocities for objects one and two.
m1 and m2 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
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?

45. 2. The cannon is 100kg and the cannonball is 5 kg
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 Firing m1v1 + m2v2 = m1fv1f + m2fv2f
Before Firing After Firing m1v1 + m2v2 = m1fv1f + m2fv2f 0 = (100kg)vcf + (5kg)(100m/s) kgm/s = (100 kg) vcf m/s = vcf recoil velocity of cannon

47. 3. A 63-kg astronaut is in spacewalk when the tether breaks
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?
(4 kg)

51. Bg fish sm.fish Bg fish sm.fish
m1v 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

52. Find the final velocity of the cart and brick together
4. A 2 kg brick not moving horizontally is dropped on a 3 kg cart moving at 5.0 m/s.
Find the final velocity of the cart and brick together

53. cart. brick. cart. brick m1v1 + m2v2 = m1fv1f + m2fv2f (3kg)(5
cart brick cart brick m1v1 + m2v2 = m1fv1f + m2fv2f (3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v kg m/s = v (3kg + 2 kg) (150 kg m/s )/5 kg = 3.0 m/s
aaa

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

55. Which is totally elastic? Inelastic?

56. 6. A 1000 kg car moving east at 20 m/s rear ends a stationary truck
6. A 1000 kg car moving east at 20 m/s rear ends a stationary truck. The truck’s mass is 3000-kg. If the bumpers lock on impact, what is the final velocity of truck/car wreck?
Inelastic Collision mc = 1000 kg mt = 3000 kg vc = 20 m/s vt = 0 pc = pt =

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

58. Elastic Collision mc = 1000 kg. mt = 3000 kg vc. = 20 m/s. vt. =. 0 7
Elastic Collision mc = 1000 kg mt = 3000 kg vc = 20 m/s vt = Find final velocity of the car if truck has final velocity of 10 m/s.

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

60. Do Now: On July 4th my family likes to shoot off fireworks
Do Now: On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point. Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes: How does the rocket’s momentum compare before & after the explosion? How does its KE compare compare before & after the explosion?

61. Inelastic Collisions Stick em together KE “lost” converted Elastic Collisions – no KE lost. Bounce off each other.

62. Hwk Read Rev Book pg 57 – 58 Do sheet 1-8

63. Hwk Prob’s in momentum sheet
Film Understanding Car Crashes 23 min
Hwk Prob’s in momentum sheet

64. Fish lunch Hewitt 4:00 https://www.youtube.com/watch?v=MK0B5hEU7OI
Hewitt Cons Momentum 6:30
Fish lunch Hewitt 4:00