Conservation of Linear Momentum Lab Report

sConservation of Linear Momentum Dustin Buenaventura, Kim Lambert Cabaobao, Elben Joseph Camama, Mariya Dennise Concepcion, John Paoleo Dona, Sharele Ebrada, Christian Albert Factoran Group 2 Friday / 7-10 P.M. / OZ 309 Physics Department, Adamson University, Ermita, Manila

Abstract This experiment tends to study the primary of conservation of linear momentum on one dimension. Formulating a formula for

1. Introduction 2. Linear momentum is defined as the product of the mass and the velocity. It is a vector quantity and its direction is exactly the same as that of the velocity. Unlike energy, momentum is not transformed from one form into another: momentum remains momentum and is conserved in all processes. For any system of physical objects, the linear momentum is conserved provided that no outside forces act upon that system. This requirement that the system be isolated is reminiscent of our requirement for mechanical energy conservation. When we design an experiment to demonstrate the conservation of momentum, we attempt to insure that the collisions are completely elastic or completely inelastic, and that no external forces act on our well defined colliding system. The conservation of momentum law states that, in the absence of external forces, the total momentum of a system does not change. 3. The basic idea is to come up with one or more equations that allow us to predict the final velocities in a system of colliding objects, based on our knowledge of the initial masses and velocities of the collision partners. The measurements will allow us to extract the velocities of our collision partners before and after they collide with each other. The measured initial velocities can be used to calculate predicted final velocities. These predicted final velocities can then be compared to the final velocities you actually observe in order to test the conservation of momentum law.

4. Theory 5. Momentum: The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: 6.

p=mv

7. Linear momentum is a vector quantity because it equals the product of a scalar quantity m and a vector quantity v. Its direction 8. is along v, it has dimensions ML/T, and its SI unit is kg E m/s. Using Newton fs second law of motion, we can relate the linear momentum of a particle to the resultant force acting on the particle. We start with the Newtonfs second law and substitute the definition of acceleration: 9.

f =ma

10. This shows that the time rate of change of the linear momentum of a particle is equal to the net force acting on the particle. The impulse of the force F acting on a particle equals the change in the momentum of the particle. From the Newtonfs second Law, 11. Impulse is defined as: 12.

I=f ∗∆ t

13. ` When we say that an impulse is given to a particle, we mean that momentum is transferred from an external agent to that particle. 14. 15. Conservation of Momentum: For a system consisting of multiple masses, the total momentum of the system is given by; 16.

m1 v 1+ m2 v 2=m1 v '1 +m2 v 2 ' (1)

17. where “M” is the total mass of the system and “v” is the speed of the center of mass. The total momentum of a system of n particles is equal to the multiplication of the total mass of the system and the speed of the center of mass. So long as the net force on the entire system is zero, the total momentum of the system remains constant (conserved). This is called the conservation of linear momentum. Although the momentums of the each particle in the system changes, total momentum remains constant.

v=

18.

19. t=

|

difference= 20.

√

x t

2H g

the time in which by the computed time the group can get the velocity of each ball. After computing for the velocity, the group finally can get the initial and final momentum with the help of the computed and the formula for the momentum. 31. 32. Results and Discussion 33. This part of the dissertation shows and discusses the result of the experimentation. The result is shown in the table below 34. Table 1: First Pair of Ball

(2)

35. Mass Ball 1 (gm) 37. Mass Ball 2 (gm) 39. Time (s) 41. Height (cm)

(3)

p 1−( p1 ' + p'2 ) p1+ ( p1 ' + p'2 ) 2

|

36. 3.5 38. 8.4 40. 0.259 42. 32.9

43.

∗100 (4)

21. Collisions: If two bodies collide with each other, they apply a big force to each other in a very short time interval. 22. 23. Methodology 24. 25. The group used the following materials: metal stand with clamp, 4metal balls with different sizes, meter stick, ramp, carbon paper, scotch tape and a bond paper. 26. 27. 28. Set up:

46. Tot al initi al mo me ntu m 52. Ball 1

47. Total final 48. momentum

53. Bal l1

54. Ball 2

55.

p1+ p 2 ' 56. g

61.

63. 65. 67.

v1

69. 71. 73.

75.

77. 78.

p1 x 1 ' v 1 ' p1 ' x 2 ' v 2 ' p2 '

62.

64. 66. 68.

70. 72. 74.

76.

cm

g

g

g

cm

cm

81. 13

83. 85. 87. 4 8.4 32 86. 82. 84. 88. 102. 104.106. 108. 12 4 7.8 30 107. 103. 105. 109.

cm

cm

89. 91. 93. 1 12 48

95. 4

90. 92. 94. 96. 110. 112. 114. 116. 1 11 44 3

97. 98. 8 13

118. 119. 8 8.

111. 113. 115. 117.

120. 121. 29. 30. The group was assigned to determine the total and final initial momentum of four different ball sizes. Using the computed mass and the measured height the group able to get

49. % 50. Di

Table2: Second Pair of Balls

122.

Mass Ball1 (gm)

124.

Mass Ball2 (gm)

125.64.5

Time(s)

127.0.259

126.

128.Height(cm)

130.

123.24.7

129.32.9

3.

1.

4.

5.

16.

131. 132. T he data you 6. found in the first D two tables was used to calculate Ball 1 9. Ball 1 10. Ball 2 11. 13. the first two balls p1+ p 2 'in which the group used the 12. smaller ball as g the first mass 17. 19. 21. 23. 25. 27. 29. 31. 33. 34. while the other bigger ball was v1 p1 x 1 ' v 1 ' p1 ' x 2 ' v 2 ' p2 ' used as the 18. 20. 22. 24. 26. 28. 30. 32. second ball.

c

c

2. T

8.

15.

x1

Total initial moment um

g

Total final momentum

%

c

c

g

c

c

g

35. 36. 37.

39. 41. 43.

45. 47. 49.

51.

53. 54.

1

1

3

1

4

1

1

6

4

7

38.

40.

42.

44.

46.

48.

50.

52.

3

55. 56. 58. 2

5

60. 62. 64.

66. 68. 70.

72.

74. 75.

3

1

3

1

4

1

1

7

4

7

57.

59.

61.

63.

65.

67.

69.

71.

73.

5