Forest UCM Energy PE n ConsForces - Revision history

Foretony: /* conservation of mechanical enegy */

2021-09-23T22:14:30Z

conservation of mechanical enegy

2021-09-22T17:13:45Z

Aside on non-conservative Lorentz force

2014-09-23T22:09:39Z

Example: Show that a the force on a charge by an electric field is conservative

2014-09-23T22:09:19Z

Example: Show that a the force on a charge by an electric field is conservative

2014-09-23T22:07:31Z

Example: Show that a the force on a charge by an electric field is conservative

2014-09-23T22:03:45Z

Potential Energy

2014-09-22T18:53:58Z

Frictional force example

2014-09-22T18:47:11Z

conservation of mechanical enegy

2014-09-22T18:45:45Z

Potential Energy

2014-09-22T18:44:56Z

Frictional force example

@@ Line 75: / Line 75: @@
 :<math>U = -qE_0x</math>
-= conservation of mechanical enegy =
+= conservation of mechanical energy =
 Let

@@ Line 139: / Line 139: @@
 =Aside on non-conservative Lorentz force=
-Given the experience of air frictions dependence on velocity,  classical mechanic may argue that the velocity dependence of the Lorentz Force's magnetic term is also non-conservative
+Given the experience of air friction's dependence on velocity,  classical mechanic may argue that the velocity dependence of the Lorentz Force's magnetic term is also non-conservative
 for example:

@@ Line 71: / Line 71: @@
 :<math>\Delta U = -W = -qE_0 (x_2 - x_1)</math>
-You can define a potential energy U with respect to an arbitrary reference point (x=0) such that
+You can define a potential energy U with respect to an arbitrary reference point <math>(x_1=0)</math> such that
 :<math>U = -qE_0x</math>

← Older revision		Revision as of 22:09, 23 September 2014
Line 66:		Line 66:

	Since the work done by the above force only depends on the endpoints (<math>x_1</math> and <math>x_2</math>) the force is conservative.		Since the work done by the above force only depends on the endpoints (<math>x_1</math> and <math>x_2</math>) the force is conservative.
		+
		+	The change in the potential energy is then
		+
		+	:<math>\Delta U = -W = -qE_0 (x_2 - x_1)</math>
		+
		+	You can define a potential energy U with respect to an arbitrary reference point (x=0) such that
		+
		+	:<math>U = -qE_0x</math>

	= conservation of mechanical enegy =		= conservation of mechanical enegy =

← Older revision		Revision as of 22:07, 23 September 2014
Line 58:		Line 58:

	:<math>\Rightarrow \vec{F} = q E_0 \hat i</math>		:<math>\Rightarrow \vec{F} = q E_0 \hat i</math>
		+
		+
		+	The work done moving the charge between two points, point 1 and point 2, using the above force is
		+
		+	:<math>W = \int_1^2 \vec{F} \cdot d \vec r = q E_0 \int_1^2 \hat i \cdot d \vec r</math>
		+	::<math>= \int_1^2 dx = qE_0 (x_2 - x_1)</math>
		+
		+	Since the work done by the above force only depends on the endpoints (<math>x_1</math> and <math>x_2</math>) the force is conservative.

	= conservation of mechanical enegy =		= conservation of mechanical enegy =

@@ Line 50: / Line 50: @@
 :Positive Work INcreases the kinetic energy (T) but DEcreases the Potential energy (U)
 :Negative Work DEcreases the kinetic energy (T) but INcreases the Potential energy (U)
 = conservation of mechanical enegy =

@@ Line 109: / Line 109: @@
 :<math>\Delta T - W_{cons} = W_{non-cons}</math>
 :<math>\Delta T + \Delta U = W_{non-cons}</math>
 =Aside on non-conservative Lorentz force=

@@ Line 73: / Line 73: @@
 since
-:<math>\Delta T = \int_{r_1}^{r_2} \vec{F}(\vec r) \cdot dr</math>
+:<math>\Delta T = W</math>
 :: <math> = -\Delta U</math>

@@ Line 32: / Line 32: @@
 Then a potential energy U(r) may be defined such that the total energy of the system is constant (conserved)
-: <math>E_{tot} = T + U(r) =</math> constant
+: <math>\Delta E_{tot} = \Delta T + \Delta U(r) =</math> constant
 where
-:<math>U(r) \equiv -\int_{r_o}^r \vec{F}(r) \cdot d\vec{}r = - W_{cons}</math>
+:<math>\Delta U(r) \equiv -\int_{r_o}^r \vec{F}(r) \cdot d\vec{}r = - W_{cons}</math>
 and

← Older revision		Revision as of 18:44, 22 September 2014
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	:<math>\Delta T - W_{cons} = W_{non-cons}</math>		:<math>\Delta T - W_{cons} = W_{non-cons}</math>
		+	:<math>\Delta T + \Delta U = W_{non-cons}</math>

	=Aside on non-conservative Lorentz force=		=Aside on non-conservative Lorentz force=