Forest UCM Ch3 CoM - Revision history

Foretony: /* Example 2: CM of a flat disk */

2014-09-15T01:09:06Z

Example 2: CM of a flat disk

2014-09-15T00:40:33Z

Where does the second piece land

2014-09-15T00:39:56Z

Problem 3-19 Projectile explodes in midair

2014-09-15T00:14:34Z

Problem 3-19 Projectile explodes in midair

2014-09-14T23:52:08Z

Problem 3-19 Projectile explodes in midair

2014-09-14T23:28:53Z

Problem 3-19 Projectile explodes in midair

2014-09-14T23:28:30Z

Problem 3-19 Projectile explodes in midair

2014-09-14T23:27:26Z

Problem 3-19

2014-09-14T23:16:47Z

Example 2: CM of a flat disk

2014-09-14T23:14:29Z

Example 2: CM of a flat disk

@@ Line 35: / Line 35: @@
 =Example 2: CM of a flat disk=
-Find the center of mass for a disk of radius <math>R</math> and area mass density <math>\rho=m/A</math>
+Find the center of mass for a disk of radius <math>R</math> and area mass density <math>\sigma=m/A</math>
-:<math>x_{cm} = \frac{1}{m} \int x \rho dA = \frac{1}{m} \int x \rho r dr d\theta</math>
+:<math>x_{cm} = \frac{1}{m} \int x \sigma dA = \frac{1}{m} \int x \sigma r dr d\theta</math>
-::<math>= \frac{\rho}{m}\int r \cos \theta r dr d\theta</math>
+::<math>= \frac{\sigma}{m}\int r \cos \theta r dr d\theta</math>
 ::<math>= \frac{1}{A}\int  r^2 dr \int d(\sin \theta)</math>
 ::<math>= \frac{1}{A}\int  r^2 dr \left . \sin \theta \right |_0^{2\phi}</math>

@@ Line 89: / Line 89: @@
 : <math>100 = \frac{150m + xm}{2m}</math>
 :<math>x = \frac{200 m -150 m }{m} = 50</math>
 [[Forest_UCM_MnAM#Center_of_Mass]]

@@ Line 80: / Line 80: @@
-Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away.   On its way to the target the projectile breaks up into two pieces.  One piece lands 100m behind the target.
+Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away.   On its way to the target the projectile breaks up into two EQUAL pieces.  One piece lands 50m beyond the target.
 ==Where does the second piece land==
 [[Forest_UCM_MnAM#Center_of_Mass]]

@@ Line 82: / Line 82: @@
 Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away.   On its way to the target the projectile breaks up into two pieces.  One piece lands 100m behind the target.
-==Where does the secondpiece land==
+==Where does the second piece land==
 [[Forest_UCM_MnAM#Center_of_Mass]]

← Older revision		Revision as of 23:52, 14 September 2014
Line 80:		Line 80:


−	Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away.	+	Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away. On its way to the target the projectile breaks up into two pieces. One piece lands 100m behind the target.
		+
		+	==Where does the secondpiece land==


	[[Forest_UCM_MnAM#Center_of_Mass]]		[[Forest_UCM_MnAM#Center_of_Mass]]

← Older revision		Revision as of 23:28, 14 September 2014
Line 80:		Line 80:


−	Suppose a projectile of mass M is fired to hit a target that is 100 m away.	+	Suppose a projectile of mass <math>M</math> is fired to hit a target that is 100 m away.


	[[Forest_UCM_MnAM#Center_of_Mass]]		[[Forest_UCM_MnAM#Center_of_Mass]]

← Older revision		Revision as of 23:28, 14 September 2014
Line 79:		Line 79:
	=Problem 3-19 Projectile explodes in midair=		=Problem 3-19 Projectile explodes in midair=

		+
		+	Suppose a projectile of mass M is fired to hit a target that is 100 m away.


	[[Forest_UCM_MnAM#Center_of_Mass]]		[[Forest_UCM_MnAM#Center_of_Mass]]

@@ Line 77: / Line 77: @@
 ::<math>=  \frac{4R^3}{3\pi} </math>
-=Problem 3-19=
+=Problem 3-19 Projectile explodes in midair=
 [[Forest_UCM_MnAM#Center_of_Mass]]