imported>Patrick: Created page with 'The mass of the third piece is (6 - 3 - 2)kg = 1 kg. We will compute the components of the linear momentum of the bomb, $p_b$ , the 1-kg piece, $p_1$ , the 2-…'

2011-09-13T20:11:28Z

Created page with 'The mass of the third piece is (6 - 3 - 2)kg = 1 kg. We will compute the components of the linear momentum of the bomb, <math>p_b</math>, the 1-kg piece, <math>p_1</math>, the 2-…'

New page

The mass of the third piece is (6 - 3 - 2)kg = 1 kg. We will compute the components of the linear momentum of the bomb, <math>p_b</math>, the 1-kg piece, <math>p_1</math>, the 2-kg piece, <math>p_2</math>, and the 3-kg piece, <math>p_3</math>. The linear momentum is conserved. We predict that the vector <math>p_3</math> must be in the 4th quadrant so that <math>p_b = p_1 + p_2 + p_3</math>. 
[[image:Helena_Conserv_Mom_Ex_5_Soln.png|TOP]] 

{| border="1" cellpadding="2" style="text-align:center"
|-
! Momentum
! x-component
! y-component
|-
! <math>p_b</math>
| <math>(6)(5) \cos(-37^{\circ}) = 24 \tfrac{kg m}{s}</math>
| <math>(6)(5) \sin(-37^{\circ}) = 18 \tfrac{kg m}{s}</math>
|-
! <math>p_1</math>
| <math>{p_1}_x</math>
| <math>{p_1}_y</math>
|-
! <math>p_2</math>
| <math>-(2)(3) = -6 \tfrac{kg m}{s}</math>
| 0
|-
! <math>p_3</math>
| <math>(3)(2) \cos(53^{\circ}) = 3.6 \tfrac{kg m}{s}</math>
| <math>(3)(2) \sin(53^{\circ}) = 4.8 \tfrac{kg m}{s}</math>
|}
 
Then we write the equations
 
<math>p_{{before}_x} = p_{{after}_x}</math>

<math>24 = {p_1}_x - 6 + 3.6</math>

<math>{p_1}_x = 26.4 \tfrac{kg m}{s}</math>
 
and
 
<math>p_{{before}_y} = p_{{after}_y}</math>

<math>-18 = {p_1}_y + 0 + 4.8</math>

<math>{p_1}_y = -22.8 \tfrac{kg m}{s}</math>
 
To obtain the velocity of the third fragment, we divide its momentum by its mass (1 kg):

<math>\vec{v} = 26.4 \hat{i} - 22.8 \hat{j}</math>

We note that our prediction was right. The linear momentum of the third piece is in the fourth quadrant.

Conservation of Momentum EX 5 - Revision history

imported>Patrick: Created page with 'The mass of the third piece is (6 - 3 - 2)kg = 1 kg. We will compute the components of the linear momentum of the bomb, p_b, the 1-kg piece, p_1, the 2-…'

imported>Patrick: Created page with 'The mass of the third piece is (6 - 3 - 2)kg = 1 kg. We will compute the components of the linear momentum of the bomb, $p_b$ , the 1-kg piece, $p_1$ , the 2-…'