imported>Patrick: Created page with 'Given that $\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3$ , we will choose a coordinate system and determine the angles with the x-axis.

[[image:Helena_Co…'

2011-08-30T18:27:18Z

Created page with 'Given that <math>\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3</math>, we will choose a coordinate system and determine the angles with the x-axis. [[image:Helena_Co…'

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Given that <math>\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3</math>,

we will choose a coordinate system and determine the angles with the x-axis. 
[[image:Helena_Conserv_Mom_Ex_3_Soln.png|TOP]] 

Then we will compute the components of all vectors:

{| border="1" cellpadding="2" style="text-align:center"
|-
! Momentum
! x-component
! y-component
|-
! <math>p_1</math>
| 96 cos(37°) = 83.1 <math>\tfrac{kg m}{s}</math>
| 96 sin(37°) = -48 <math>\tfrac{kg m}{s}</math>
|-
! <math>p_2</math>
| 167 cos(53°) = 100.5 <math>\tfrac{kg m}{s}</math>
| 167 cos(53°) = 133.4 <math>\tfrac{kg m}{s}</math>
|-
! <math>p_3</math>
| <math>p_3</math> cos(240) = -0.5 <math>p_3</math>
| <math>p_3</math> sin(240) = -0.87 <math>p_3</math>
|-
! <math>p_{net}</math>
| <math>p_{net}</math>
| 0
|}
 
This allows us to write an equation for x-component

<math>p_{net} = 83.1 + 100.5 - 0.5 p_3</math>
 
and y-component

<math>0 = -48 + 133.4 - 0.87 p_3</math>
 
Solving the second equation first, we find

<math>p_3 = \frac{48 - 133.4}{-0.87} = 98.2 \tfrac{kg m}{s}</math>
 
Then we solve the first equation to find

<math>p_{net} = 100.5 + 83.1 - 0.5(98.2) = 134.5 \tfrac{kg m}{s}</math>
 
From this equation we conclude that the total momentum has a magnitude 134.5 <math>\tfrac{kg m}{s}</math> and points East since its x-component is positive. We also conclude that the magnitude of the momentum of the third particle is <math>98.2 \tfrac{kg m}{s}</math>.

Conservation of Momentum EX 3 - Revision history

imported>Patrick: Created page with 'Given that \vec{p}_{net} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3, we will choose a coordinate system and determine the angles with the x-axis. [[image:Helena_Co…'

imported>Patrick: Created page with 'Given that $\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3$ , we will choose a coordinate system and determine the angles with the x-axis.

[[image:Helena_Co…'