Forest UCM MnAM ElasticCol - Revision history

Foretony: /* Example: problem 3.5 */

2014-09-12T12:24:21Z

Example: problem 3.5

2014-09-12T12:23:19Z

Example: problem 3.5

2014-09-12T12:20:37Z

Example: problem 3.5

2014-09-12T12:19:13Z

Example: problem 3.5

2014-09-12T12:18:23Z

Example: problem 3.5

2014-09-12T12:18:07Z

Example: problem 3.5

2014-09-12T12:16:24Z

Example: problem 3.5

2014-09-12T12:16:03Z

Example: problem 3.5

2014-09-12T12:15:36Z

Example: problem 3.5

2014-09-12T12:15:17Z

Example: problem 3.5

← Older revision		Revision as of 12:24, 12 September 2014
Line 38:		Line 38:

	;unless one ball has a final velocity of zero		;unless one ball has a final velocity of zero
−	It can happen that the ball with an initial velocity comes to rest after hitting the second ball.	+	It can happen that the ball with an initial velocity comes to rest after hitting the second ball. To conserve momentum the second ball that was initially at rest must now move with the same momentum as the first ball.

@@ Line 35: / Line 35: @@
 :<math>\vec{v}_1^{\;\prime} \cdot  \vec{v}_2^{\;\prime} = 0 </math>
-or the balls make an angle of 90 degrees with repect to eachother
+or the balls make an angle of 90 degrees with repect to eachother.
 [[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]

@@ Line 29: / Line 29: @@
 :<math>\vec{v}_1 \cdot \vec{v}_1 =  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right ) \cdot  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right )</math>
 :<math>v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2 + 2  \vec{v}_1^{\;\prime} \cdot  \vec{v}_2^{\;\prime}</math>
 [[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]

@@ Line 28: / Line 28: @@
 :<math>\vec{v}_1 =  \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}</math>: balls have equal masses
 :<math>\vec{v}_1 \cdot \vec{v}_1 =  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right ) \cdot  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right )</math>
+:<math>v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2 + 2  \vec{v}_1^{\;\prime} \cdot  \vec{v}_2^{\;\prime}</math>
 [[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]

@@ Line 27: / Line 27: @@
 :<math>\vec{v}_1 =  \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}</math>: balls have equal masses
-:<math>\vec{v}_1 \cd0t \vec{v}_1 =  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right ) \cdot  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right )</math>
+:<math>\vec{v}_1 \cdot \vec{v}_1 =  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right ) \cdot  \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right )</math>
 [[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]

← Older revision		Revision as of 12:18, 12 September 2014
Line 24:		Line 24:
	:<math>v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2</math>		:<math>v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2</math>

		+	If I look at the dot product of the conservation of momentum equation
		+
		+	:<math>\vec{v}_1 = \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}</math>: balls have equal masses
		+	:<math>\vec{v}_1 \cd0t \vec{v}_1 = \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right ) \cdot \left ( \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}\right )</math>



	[[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]		[[Forest_UCM_MnAM#Elastic_Collision_of_2_bodies]]

@@ Line 14: / Line 14: @@
 ;Conservation of momentum
-:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\prime} +m_2 \vec{v}_2^{\;\prime}</math>
+:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\;\prime} +m_2 \vec{v}_2^{\;\prime}</math>
 :<math>m_1 \vec{v}_1 = m_1 \vec{v}_1^{\;\prime} +m_2 \vec{v}_2^{\;\prime}</math>: ball 2 has zero velocity
 :<math>\vec{v}_1 =  \vec{v}_1^{\;\prime} + \vec{v}_2^{\;\prime}</math>: balls have equal masses
@@ Line 21: / Line 21: @@
 ;Conservation of energy
-:m_1 v_1^2 + m_2 v_2^2 = m_1 \left(v_1^{\prime}\right)^2 + m_2\left(v_2^{\prime}\right)^2
+:<math>m_1 v_1^2 + m_2 v_2^2 = m_1 \left(v_1^{\prime}\right)^2 + m_2\left(v_2^{\prime}\right)^2</math>
-:v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2
+:<math>v_1^2 = \left(v_1^{\prime}\right)^2 + \left(v_2^{\prime}\right)^2</math>

@@ Line 14: / Line 14: @@
 ;Conservation of momentum
-:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\prime} +m_2 \vec{v}_2^{;;\prime}</math>
+:<math>m_1 \vec{v}_1 + m_2 \vec{v}_2= m_1 \vec{v}_1^{\prime} +m_2 \vec{v}_2^{\;\;\prime}</math>
-:<math>m_1 \vec{v}_1 = m_1 \vec{v}_1^{;\prime} +m_2 \vec{v}_2^{\prime}</math>: ball 2 has zero velocity
+:<math>m_1 \vec{v}_1 = m_1 \vec{v}_1^{\;\prime} +m_2 \vec{v}_2^{\prime}</math>: ball 2 has zero velocity
-:<math>\vec{v}_1 =  \vec{v}_1^{;;;\prime} + \vec{v}_2^{\prime}</math>: balls have equal masses
+:<math>\vec{v}_1 =  \vec{v}_1^{\;\;\;\prime} + \vec{v}_2^{\prime}</math>: balls have equal masses