Forest UCM PnCP - Revision history

Foretony: /* Newton's second law */

2014-09-08T17:45:57Z

Newton's second law

2014-09-08T11:38:49Z

Newton's second law

2014-09-08T11:38:04Z

Newton's second law

2014-09-08T11:36:53Z

Newton's second law

2014-09-08T11:31:22Z

Newton's second law

2014-09-01T11:42:39Z

Projecile Motion

2014-08-31T14:13:23Z

Another block on incline example

2014-08-31T14:07:37Z

Charged Particle in uniform B-Field

2014-08-31T14:05:36Z

quadratic friction

2014-08-31T14:05:17Z

Example: falling object with quadratic air friction

@@ Line 30: / Line 30: @@
 :<math>F_f = cv^2 = \gamma D^2 v^2 = \left ( 2.5 \times 10^{-1} \frac{N \cdot s^2}{m^4}\right ) D^2 v^2</math>
-:<math>\frac{F_f(\mbox{linear})}{F_f(\mbox{quadratic})} = \left (1.6 \times 10 ^{3} \frac{s}{m^2} \right ) D v</math>
+:<math>\frac{F_f(\mbox{Quadratic})}{F_f(\mbox{linear})} = \left (1.6 \times 10 ^{2} \frac{s}{m^2} \right ) D v</math>
 Thus in order for the above ratio to be near unity,<math> Dv < 10^{-3} \Rightarrow</math> D is very small like a raindrop and has a small velocity < 1 m/s.

@@ Line 30: / Line 30: @@
 :<math>F_f = cv^2 = \gamma D^2 v^2 = \left ( 2.5 \times 10^{-1} \frac{N \cdot s^2}{m^4}\right ) D^2 v^2</math>
-:<math>\frac{F_f(\mbox{linear})}{F_f(\mbox{quadratic})} = \right (1.6 \times 10 ^{3} \frac{s}{m^2} \left ) D v</math>
+:<math>\frac{F_f(\mbox{linear})}{F_f(\mbox{quadratic})} = \left (1.6 \times 10 ^{3} \frac{s}{m^2} \right ) D v</math>
 Thus in order for the above ratio to be near unity,<math> Dv < 10^{-3} \Rightarrow</math> D is very small like a raindrop and has a small velocity < 1 m/s.

@@ Line 30: / Line 30: @@
 :<math>F_f = cv^2 = \gamma D^2 v^2 = \left ( 2.5 \times 10^{-1} \frac{N \cdot s^2}{m^4}\right ) D^2 v^2</math>
-:<math>\frac{F_f(\mbox{linear})}{F_f{\mbox{quadratic})} = \right (1.6 \times 10 ^{3} \frac{s}{m^2} \left ) D v</math>
+:<math>\frac{F_f(\mbox{linear})}{F_f(\mbox{quadratic})} = \right (1.6 \times 10 ^{3} \frac{s}{m^2} \left ) D v</math>
 Thus in order for the above ratio to be near unity,<math> Dv < 10^{-3} \Rightarrow</math> D is very small like a raindrop and has a small velocity < 1 m/s.

@@ Line 26: / Line 26: @@
 ;Linear:
-:<math>F_f = bv = \beta D v = 1.6 \times 10^{-4} \frac{N \cdot s}{m^2} D v</math>
+:<math>F_f = bv = \beta D v = \left ( 1.6 \times 10^{-4} \frac{N \cdot s}{m^2}\right ) D v</math>
 ==Linear Air Resistance==

← Older revision		Revision as of 11:31, 8 September 2014
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	Air resistance for rain drops or ball bearings in oil tends to be more linear while canon balls and people falling through the air tends to be more quadratic.		Air resistance for rain drops or ball bearings in oil tends to be more linear while canon balls and people falling through the air tends to be more quadratic.
		+
		+
		+	Example: A Sphere moving through air at STP
		+
		+	;Linear:
		+	:<math>F_f = bv = \beta D v = 1.6 \times 10^{-4} \frac{N \cdot s}{m^2} D v</math>

	==Linear Air Resistance==		==Linear Air Resistance==

← Older revision		Revision as of 11:42, 1 September 2014
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	=Projecile Motion=		=Projecile Motion=
		+
		+	[[Forest_UCM_PnCP_ProjMotion]]

	=Charged Particle in uniform B-Field=		=Charged Particle in uniform B-Field=

← Older revision		Revision as of 14:13, 31 August 2014
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	[[Forest_UCM_NLM_BlockOnIncline]]		[[Forest_UCM_NLM_BlockOnIncline]]
		+
		+	=Projecile Motion=

	=Charged Particle in uniform B-Field=		=Charged Particle in uniform B-Field=

@@ Line 37: / Line 37: @@
 =Charged Particle in uniform B-Field=
-Consider a charged particle moving the x-y plane in the presence of a uniform magnetic field with field lines in the z-dierection.
+[[Forest_UCM_PnCP_QubUniBfield]]
 [[Forest_Ugrad_ClassicalMechanics]]

← Older revision		Revision as of 14:05, 31 August 2014
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	[[Forest_UCM_PnCP_QuadAirRes]]		[[Forest_UCM_PnCP_QuadAirRes]]
−
−	~~Consider a ball falling under the influence of gravity and a frictional force that is proportion to its velocity squared~~
−
−	~~:<math>\sum \vec{F}_{ext} = mg -bv^2 = m \frac{dv}{dt}</math>~~
−
−	~~Find the fall distance~~
−
−	~~Here is a trick to convert the integral over time to one over distance so you don't need to integrate twice as inthe previous example~~
−
−	~~:<math>\frac{dv}{dt} = \frac{dv}{dy}\frac{dy}{dt} = v\frac{dv}{dy}</math>~~
−
−	~~The integral becomes~~
−
−	~~:<math>mg -bv^2 = m v\frac{dv}{dy}</math>~~
−	~~:<math>\int_{y_i}^{y_f} dy = \int_{v_i}^{v_f} m \frac{dv}{\left ( mg -bv^2 \right ) }</math>~~
−	~~:<math>y = \int_{v_i}^{v_f} \frac{dv}{\left ( g -\frac{b}{m}v^2 \right ) }</math>~~
−
−
−	~~let <math>u = g -\frac{b}{m}v^2</math>~~
−
−	~~then <math>du = -2\frac{b}{m}v dv</math>~~
−
−	~~:<math>y =\int_{v_i}^{v_f} \frac{-m}{2b} \frac{du}{u } = \frac{b}{m} \int_{v_f}^{v_i} \ln {g -\frac{b}{m}v^2} =</math>~~
−	~~:<math>y =\frac{m}{2b} \ln \left ( \frac {g -\frac{b}{m}v_i^2}{g -\frac{b}{m}v_f^2} \right ) </math>~~

	==Another block on incline example==		==Another block on incline example==

@@ Line 26: / Line 26: @@
 [[Forest_UCM_PnCP_LinAirRes]]
-==Example: falling object with quadratic  air friction==
+==quadratic friction==
-[[Forest_UCM_PnCP_LinAirRes]]
+[[Forest_UCM_PnCP_QuadAirRes]]
 Consider a ball falling under the influence of gravity and a frictional force that is proportion to its velocity squared