Forest UCM NLM AtwoodMachine - Revision history

Foretony: /* Solutions */

2014-08-22T12:52:58Z

Solutions

2014-08-22T12:52:42Z

Solutions

2014-08-22T12:51:49Z

Solutions

2014-08-22T12:50:57Z

Solutions

2014-08-22T12:49:33Z

Solutions

2014-08-22T12:47:43Z

Solutions

2014-08-22T12:46:29Z

Solutions

2014-08-22T12:42:21Z

Solutions

2014-08-22T12:31:23Z

3 equations and 3 unknowns

2014-08-22T12:28:50Z

3 euqations and 3 unknowns

@@ Line 122: / Line 122: @@
 & -m_1 & m_1g \\
 & m_2 & m_2g \\
-& 0 & -m_3g \end{array} \right|}{\left| \begin{array}{ccc}
+& 0 & m_3g \end{array} \right|}{\left| \begin{array}{ccc}
 & -m_1 & m_1 \\
 & m_2 & m_2 \\

@@ Line 119: / Line 119: @@
-:<math>a_3 = \frac{\left( \begin{array}{ccc}
+:<math>a_3 = \frac{\left| \begin{array}{ccc}
 & -m_1 & m_1 \\
 & m_2 & m_2 \\
-& 0 & -m_3 \end{array} \right)}{\left( \begin{array}{ccc}
+& 0 & -m_3 \end{array} \right|}</math>
 [[Forest_UCM_NLM#Atwoods_Machine]]

← Older revision		Revision as of 12:51, 22 August 2014
Line 116:		Line 116:
	</math>		</math>

		+	Cramer's Rule:
		+
		+
		+	:<math>a_3 = \frac{\left( \begin{array}{ccc}
		+	1 & -m_1 & m_1 \\
		+	1 & m_2 & m_2 \\
		+	2 & 0 & -m_3 \end{array} \right)}{\left( \begin{array}{ccc}
		+	1 & -m_1 & m_1 \\
		+	1 & m_2 & m_2 \\
		+	2 & 0 & -m_3 \end{array} \right)}</math>

	[[Forest_UCM_NLM#Atwoods_Machine]]		[[Forest_UCM_NLM#Atwoods_Machine]]

@@ Line 107: / Line 107: @@
 & -m_1 & m_1 \\
 & m_2 & m_2 \\
-& 0 & -m_3 \end{array} \right)
+& 0 & -m_3 \end{array} \right)\left( \begin{array}{ccc}
 </math>
 [[Forest_UCM_NLM#Atwoods_Machine]]

← Older revision		Revision as of 12:49, 22 August 2014
Line 104:		Line 104:
	;Matrix method solution (<math>T_1, a_r, a_3</math> are the unkowns)		;Matrix method solution (<math>T_1, a_r, a_3</math> are the unkowns)

		+	<math>\left( \begin{array}{ccc}
		+	1 & -m_1 & m_1 \\
		+	1 & m_2 & m_2 \\
		+	2 & 0 & -m_3 \end{array} \right)
		+	</math>
	[[Forest_UCM_NLM#Atwoods_Machine]]		[[Forest_UCM_NLM#Atwoods_Machine]]

← Older revision		Revision as of 12:47, 22 August 2014
Line 102:		Line 102:
	:<math>a_3 = \frac{4m_1m_2 -m_2m_3 -m_1m_3}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}g</math>		:<math>a_3 = \frac{4m_1m_2 -m_2m_3 -m_1m_3}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}g</math>

		+	;Matrix method solution (<math>T_1, a_r, a_3</math> are the unkowns)

	[[Forest_UCM_NLM#Atwoods_Machine]]		[[Forest_UCM_NLM#Atwoods_Machine]]

@@ Line 98: / Line 98: @@
 solving the above system of equations leads to the solutions
-:<math>a_1 = \frac{3m_2m_3 -m_1m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 - 4 m_1 m_2}g</math>
+:<math>a_1 = \frac{3m_2m_3 -m_1m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}g</math>
-:<math>a_2 = \frac{3m_1m_3 -m_2m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 - 4 m_1 m_2}g</math>
+:<math>a_2 = \frac{3m_1m_3 -m_2m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}g</math>
-:<math>a_3 = \frac{4m_1m_2 -m_2m_3 -m_1m_3}{m_1m_3 + m_2 m_3 - 4 m_1 m_2}g</math>
+:<math>a_3 = \frac{4m_1m_2 -m_2m_3 -m_1m_3}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}g</math>
 [[Forest_UCM_NLM#Atwoods_Machine]]

← Older revision		Revision as of 12:31, 22 August 2014
Line 93:		Line 93:


		+	=== Solutions===
		+
		+
		+	solving the above system of equations leads to the solutions
		+
		+	:<math>a_1 = \frac{3m_2m_3 -m_1m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}</math>
		+	:<math>a_2 = \frac{3m_1m_3 -m_2m_3 -4m_1m_2}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}</math>
		+	:<math>a_3 = \frac{4m_1m_2 -m_2m_3 -m_1m_3}{m_1m_3 + m_2 m_3 + 4 m_1 m_2}</math>


	[[Forest_UCM_NLM#Atwoods_Machine]]		[[Forest_UCM_NLM#Atwoods_Machine]]

@@ Line 82: / Line 82: @@
 :<math>a_2=-a_r-a_3</math> : if <math>m_1</math> is accelerating upwards then <math>m_2</math> is accelerating downwards
-=== 3 euqations and 3 unknowns===
+=== 3 equations and 3 unknowns===
 :<math>T_1 - m_1 g = m_1 \left ( a_r - a_3 \right )</math>