1. M.I.T. C.P. PHYSICS
MOMENTUM

3. Momentum = mass of an object x its velocity
P = mv

4. Momentum is a vector quality!

5. Sample Problem
What is the value of the momentum of a 10-kg bowling ball as it rolls down the alley at a velocity of 5 m/s?
Step 1
P = mv
Step 2
P = (10)(5)
Step 3
P = 50 kg•m/s

6. This change in momentum is called IMPULSE!
In football, a defensive player applies a force for a given amount of time to stop the momentum of the offensive player.
This change in momentum is called IMPULSE!

7. If the impulse force is large, the object’s momentum is changed quickly!
If the impulse force is small, the object’s momentum is changed slowly!

8. Deriving the Impulse Formula

9. Deriving the Impulse Formula
Impulse = Change in Momentum
F = ma
a = Δv/t
F = m•Δv/t
F • t = m •Δv

10. In boxing, riding a punch increases Time and reduces the Force of the collision.
FT = mΔv
Ft = mΔv

11. Introduction to Engineering

13. Lab: Eggstatic Over Impulse

14. Lab: Eggstatic Over Impulse
Data Chart
Mass of Zip-lock Bag & Egg 1
kilograms
Mass of Zip-lock Bag & Egg 2 & Test Material
Breakage Height
(Egg)
meters
(Egg & Test Material)

15. Lab: Eggstatic Over Impulse
Calculation Table
Calculation #
Egg
Egg & Test Material 1 2 3 4 5 6 7

16. Lab: Eggstatic Over Impulse
Egg Calculations
Calculate the time of free fall of the egg when it broke in the zip-lock bag.
T = √2d/g
Calculate the velocity of the egg right before it broke in the zip-lock bag.
v = gt

17. Calculate the momentum of the egg and the zip-lock bag before impact.
Egg Calculations
Calculate the momentum of the egg and the zip-lock bag before impact.
p = mv
Calculate the momentum of the egg and the zip-lock bag after impact.
p = mv
Calculate the change in momentum of the egg and the zip-lock bag.
Δp = mΔv

18. Calculate the impulse of the system.
Egg Calculations
Calculate the impulse of the system.
Impulse = Δp
Assuming that the impact time lasted seconds, calculate the force the egg encountered when it broke.
F = Impulse/t

19. Egg & Test Material Calculations
Calculate the time of free fall of the egg & test material when it broke in the zip-lock bag.
T = √2d/g
Calculate the velocity of the egg & test material right before it broke in the zip-lock bag.
v = gt

20. Egg & Test Material Calculations
Calculate the momentum of the egg & test material and the zip-lock bag before impact.
p = mv
Calculate the momentum of the egg & test material and the zip-lock bag after impact.
p = mv
Calculate the change in momentum of the egg & test material and the zip-lock bag.
Δp = mΔv

21. Egg & Test Material Calculations Calculate the impulse of the system.
Impulse = Δp
Using the force value you calculated for the egg, calculate the time the egg endured the impact in the test material.
t = Impulse/F

22. Lab: How Heavy Was the Rider?

23. Lab: How Heavy Was the Rider?
Given Data
Coefficient of Static Friction (u) = 0.4
Breaking Force = N
Bike Mass = 175kg

24. Lab: How Heavy Was the Rider?
Given Formulas
d = v^2/2ug
d = ½ (v1 + v2) Δt
F • t = Δp
Δp = m•Δv

25. Law of Conservation of Energy
Law on Conservation of Mass
Mass can not be created nor destroyed, only changed.
Law of Conservation of Energy
Law of Conservation of Momentum
The total momentum in a system remains constant.

26. Momentum Conservation

27. Lab: Validating the Law of Conservation of Momentum
Interactive

28. Lab: Validating the Law of Conservation of Momentum
Data Chart: Cart
Trial #
Mass
(kg)
Velocity
(m/s) 1
100 2 3
200 4 5
400 6 7
500

29. Lab: Validating the Law of Conservation of Momentum
Data Chart: Jumper
Trial #
Mass
(kg)
Velocity
(m/s) 1 50 2
100 3 4 5 6 7

30. Lab: Validating the Law of Conservation of Momentum
Calculation Chart
Trial #
p(cart)
(kg•m/s)
p(jumper) 1 2 3 4 5 6 7

31. Sample Problem 1
Consistent with Newton's third law of motion, when a rifle is fired, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is ...
more than the bullet.
less the bullet.
the same as the bullet.

32. Sample Problem 2
A 50.0-kg cart is rolling at a constant velocity of 25.0m/s. How much mass should an additional brick have in order to slow its velocity to 15.0m/s.
Step 1
m1 x v1 = m2 x v2
Step 2
(50.0)(25.0) = m2 (15.0)
Step 3
m2 = 83.3kg
Step 4
83.3kg – 50.0kg = 33.3kg

33. Explosions Even during an explosion,
the Law of Conservation of Momentum takes effect!

34. Explosions p(before) = p(after) p(before) = m1v1 + m2v2 p1 = p2
p(after) = m1v1 + m2v2
Since velocity & momentum is a vector quality, make one of the velocities negative!

35. Calculate the velocity of the pink cart after the explosion.
Sample Problem 1
Calculate the velocity of the pink cart after the explosion.
Step 1
m1v(initial) + m2v(initial) = m1v(final) + m2v(final)
Step 2
0 = (0.5)(-40) + (1.0)v(final)
Step 3
v(final) = 20m/s

36. Calculate the velocity of the pink cart after the explosion.
Sample Problem 2
Calculate the velocity of the pink cart after the explosion.
Step 1
m1v(initial) + m2v(initial) = m1v(final) + m2v(final)
Step 2
0 = (1.0)(-20) + (2.0)v(final)
Step 3
v(final) = 10m/s

37. Calculate the velocity of the pink cart after the explosion.
Sample Problem 3
Calculate the velocity of the pink cart after the explosion.
Step 1
m1v(initial) + m2v(initial) = m1v(final) + m2v(final)
Step 2
0 = (0.5)(-40) + (2.0)v(final)
Step 3
v(final) = 10m/s

38. Lab: Explosions

39. Lab: Explosions Data Chart 1 Cart Mass (kg) Distance (m) Time (s) Left
Right

40. Lab: Explosions Data Chart 2 Cart Mass (kg) Distance (m) Time (s) Left
Right

41. Lab: Explosions Calculation Chart 1 Cart Mass (kg) Velocity (m/s)
Momentum
(kg•m/s)
Left
Right

42. Lab: Explosions Calculation Chart 2 Cart Mass (kg) Velocity (m/s)
Momentum
(kg•m/s)
Left
Right

43. Collisions
During a collision, the Law of Conservation of Momentum still takes effect!

44. In an inelastic collision, two bodies collide and act as one!
Inelastic Collisions
In an inelastic collision, two bodies collide and act as one!
The total momentum of the system before the collision must equal the total momentum of the system after the collision.

45. Inelastic Collisions
The total momentum of the system before the collision must equal the total momentum of the system after the collision.

46. Inelastic Collisions

47. Inelastic Collisions

48. Determine the initial momentum of each object.
Sample Problem
Calculate the final velocity of the girl on frictionless ice after she catches the ball.
Step 1
Determine the initial momentum of each object.
p = mv
Ball = 300kg•m/hr Girl = 0

49. Determine the total momentum before impact.
Sample Problem
Step 2
Determine the total momentum before impact.
p(before) = m1v1 + m2v2
p(before) = 300kg•m/hr

50. Determine the total mass after impact.
Sample Problem
Step 3
Determine the total mass after impact.
m(total) = (m1 + m2)
m(total) = ( )
m(total) = 75kg

51. Determine the velocity after impact.
Sample Problem
Step 4
Determine the velocity after impact.
p(after) = m(total) v2
300kg•m/hr = (75) v2
v2 = 4m/s

52. Lab: Inelastic Collisions

53. Lab: Inelastic Collisions
Red Car Data Chart
Trial #
m(kg)
vi (m/s)
vf (m/s) 1
10.0 2
5.0 3 4 5
8.0 6
6.0 7
3.0

54. Lab: Inelastic Collisions
Blue Car Data Chart
Trial #
m(kg)
vi (m/s)
vf (m/s) 1 3 2 4 5
3.0 6
2.0 7
1.0

55. Lab: Inelastic Collisions
Red Car Calculation Chart
Trial #
p(before)
p(after) 1 2 3 4 5 6 7

56. Lab: Inelastic Collisions
Blue Car Calculation Chart
Trial #
p(before)
p(after) 1 2 3 4 5 6 7

57. Lab: Inelastic Collisions
Final Calculation Chart
Trial #
Total p(before)
Total p(after)
Total KE(before)
Total KE(after) 1 2 3 4 5 6 7

58. Sample Problem
A 5.0g bullet is fired upward at a velocity of 700. m/s. It hits and embeds itself into a 5.0-kg block of wood. What is the momentum of the bullet before impact?
Step 1
p = mv
Step 2
p = (.0050)(700.)
Step 3
p = 3.5kg•m/s

59. What is the momentum of the bullet after impact?
Sample Problem
What is the momentum of the bullet after impact?
Step 1
p(before) = p(after)
Step 2
3.5kg•m/s = p(after)
Step 3
p(after) = 3.5kg•m/s

60. What is the velocity of the bullet after impact?
Sample Problem
What is the velocity of the bullet after impact?
Step 1
p(after) = m(total) v(final)
Step 2
3.5kg•m/s = (5.005)v(final)
Step 3
v(final) = .70m/s

61. What is the kinetic energy of the bullet before impact?
Sample Problem
What is the kinetic energy of the bullet before impact?
Step 1
KE = ½ mv^2
Step 2
KE = (.5)(.0050)(700.)^2
Step 3
KE = 12225J

62. What is the kinetic energy of the bullet after impact?
Sample Problem
What is the kinetic energy of the bullet after impact?
Step 1
KE = ½ mv^2
Step 2
KE = (.5)( )(.70)^2
Step 3
KE = J

63. How high does the block rise after impact?
Sample Problem
How high does the block rise after impact?
Step 1
KE = PE = mgh
Step 2
1.2224J = (5.005)(9.8)h
Step 3
h = 0.025m

64. In an inelastic collision, there is no loss of momentum!
In an inelastic collision, there is a loss of kinetic energy.

65. RESEARCH PROJECT #3

66. MIDDLESEX

67. Calculate the initial momentum.
Warm Up Problem
Calculate the initial momentum.
Step 1
p (initial) = (m1 v1(initial)) + (m2 v2(initial) )
Step 2
p(initial) = (0.045)(400.) + (16) x (0)
Step 3
p(initial) = 18 kg•m/s

68. Calculate the final velocity.
Warm Up Problem
Calculate the final velocity.
Step 1
p(final) = (m1 + m2) v(final)
Step 2
18 = ( ) v(final)
Step 3
v(final) = 1.1 m/s

69. Elastic Collisions
In an elastic collision, both objects travel independently after the collision.

70. As with an inelastic collision, there is no loss of momentum in an elastic collision.

71. But unlike an inelastic collision, there is no loss of kinetic energy during an elastic collision.

72. Lab: Elastic Collisions
Interactive

73. Lab: Elastic Collisions
Red Car Data Chart
Trial #
m(kg)
vi (m/s)
vf (m/s) 1
10.0 2
5.0 3 4 5
8.0 6
6.0 7
3.0

74. Lab: Elastic Collisions
Blue Car Data Chart
Trial #
m(kg)
vi (m/s)
vf (m/s) 1 3 2 4 5
3.0 6
2.0 7
1.0

75. Lab: Elastic Collisions
Red Car Calculation Chart
Trial #
p(before)
p(after)
KE(before)
KE(after) 1 2 3 4 5 6 7

76. Lab: Elastic Collisions
Blue Car Calculation Chart
Trial #
p(before)
p(after)
KE(before)
KE(after) 1 2 3 4 5 6 7

77. Lab: Elastic Collisions
Final Calculation Chart
Trial #
Total p(before)
Total p(after)
Total KE(before)
Total KE(after) 1 2 3 4 5 6 7

78. Which ball(s) would be moving after #1 & #2 make contact?
Sample Problem 1
Which ball(s) would be moving after #1 & #2 make contact?

79. Sample Problem 2
What would be the final velocity of ball 2 after an elastic collision if ball 1’s final velocity is 0 m/s?

80. Jeff Laws
Step 1:
Calculate Initial Momentum

81. Sample Problem 2
What would be the final velocity of ball 2 after an elastic collision if ball 1’s final velocity is 0 m/s?
Step 1
Calculate the total initial momentum.
Total p(initial) = m1 v1(initial) + m2 v2(inital)
Total p(initial) = (0.25)(+2.0) + (0.25)(-0.5)
Total p(initial) = (.50) + (-.125)
Total p(initial) = .375kg•m/s

82. Step 2:
Calculate Final Velocity of Ball #2

83. Sample Problem 2
What would be the final velocity of ball 2 after an elastic collision if ball 1’s final velocity is 0 m/s?
Step 2
Calculate the final velocity of ball #2.
Total p(final) = m1 v1(final) + m2 v2(final)
.375 = (0.25)(0) + (0.25)v2(final)
.375 = (0.25)v2(final)
v(final) = 1.5m/s

84. Sample Problem 3
What would be the final velocity of ball 2 after an elastic collision if ball 1’s final velocity is -1.0 m/s?
Step 1
Calculate the total initial momentum.
Total p(initial) = m1 v1(initial) + m2 v2(inital)
Total p(initial) = (0.25)(+2.0) + (0.25)(-0.5)
Total p(initial) = (.5) + (-.125)
Total p(initial) = .375 kg•m/s

85. Sample Problem 3
What would be the final velocity of ball 2 after an elastic collision if ball 1’s final velocity is -1.0 m/s?
Step 2
Calculate the final velocity of ball #2.
Total p(final) = m1 v1(final) + m2 v2(final)
.375= (0.25)(-1.0) + (0.25)v2(final)
.375 = (-0.25) + (0.25)v2(final)
v(final) = 2.5 m/s

86. Nice Job!!!!!!!!

87. Inelastic Collisions

88. Inelastic Collisions

89. 2-Dimentional Inelastic Collisions

90. Sketch the before & after systems
Sample Problem
A 2165 kg car moving east at 17.0 m/s collides with a 1325 kg car moving north at 27.0m/s. They collide and stick together. In what direction and at what velocity do they move after the collision?
Step 1
Sketch the before & after systems

91. Calculate the initial momentum of each car.
Sample Problem
Step 2
Calculate the initial momentum of each car.
Car A (east)
p = mv
p = (2165)(17.0)
p = kg•m/s

92. Calculate the initial momentum of each car.
Sample Problem
Step 2
Calculate the initial momentum of each car.
Car B (north)
p = mv
p = (1325)(27.0)
p = kg•m/s

93. Establish the coordinate axis. tanΘ = opposite/adjacent
Sample Problem
Step 3
Establish the coordinate axis.
Car A = opposite
Car B = adjacent
tanΘ = opposite/adjacent

94. Calculate the direction of the collision. tanΘ = opposite/adjacent
Sample Problem
Step 4
Calculate the direction of the collision.
tanΘ = opposite/adjacent
tanΘ = 35800/36800
tanΘ = .973
Θ = 44.2°

95. Calculate the total momentum after the collision.
Sample Problem
Step 5
Calculate the total momentum after the collision.
a^2 + b^2 = c^2
(36800)^2 + (35800)^2 = c^2
= c^2
c = 51300kg•m/s

96. Sample Problem
Step 6
Calculate the final velocity after the collision.
p(final) = (m1 + m2)v(final)
51300 = ( )v(final)
51300 = 3490v(final)
v(final) = 14.7m/s