Terminal Speed - Revision history

YorickAndeweg: /* See also */

2019-08-06T20:38:43Z

See also

← Older revision		Revision as of 16:38, 6 August 2019
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	*[[Net Force]]		*[[Net Force]]
	*[[Projectile Motion]]		*[[Projectile Motion]]
	*[[Speed ~~and~~ Velocity]]		*[[Speed vs Velocity]]

	===Further reading===		===Further reading===

Richard.Udall: /* See also */

2019-07-25T20:19:12Z

See also

← Older revision		Revision as of 16:19, 25 July 2019
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	*[[Net Force]]		*[[Net Force]]
	*[[Projectile Motion]]		*[[Projectile Motion]]
			*[[Speed and Velocity]]

	===Further reading===		===Further reading===

Richard.Udall: /* See also */

2019-07-25T20:16:07Z

See also

← Older revision		Revision as of 16:16, 25 July 2019
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	== See also ==		== See also ==
	[[Fundamentals of Iterative Prediction with Varying Force]]		*[[Fundamentals of Iterative Prediction with Varying Force]]
			*[[Net Force]]
	[[Net Force]]		*[[Projectile Motion]]

	[[Projectile Motion]]

	===Further reading===		===Further reading===

	Anderson, John David (1997). A History of Aerodynamics and its Impact on Flying machines.		*Anderson, John David (1997). A History of Aerodynamics and its Impact on Flying machines.
			*Matter and Interactions, 4th Edition

	===External links===		===External links===
	~~http://regentsprep.org/regents/physics/phys01/terminal/default.htm~~		*[http://www.britannica.com/science/terminal-velocity Encyclopedia Britannica]
			*[https://www.grc.nasa.gov/www/k-12/airplane/termv.html NASA]
	http://www.britannica.com/science/terminal-velocity

	https://www.grc.nasa.gov/www/k-12/airplane/termv.html

	==References==		==References==

Richard.Udall: /* Middling */

2019-07-25T20:13:34Z

Middling

← Older revision		Revision as of 16:13, 25 July 2019
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	For clarity's sake, let's rederive the equation for terminal velocity by setting the force of gravity equal to the force of drag:		For clarity's sake, let's rederive the equation for terminal velocity by setting the force of gravity equal to the force of drag:

	<math> \|F_D\| = \|F_G\| \Rightarrow ~~1/2~~ C_D A \rho v^2 = m g </math>		<math> \|F_D\| = \|F_G\| \Rightarrow \frac{C_D A \rho v^2}{2} = m g </math>

	Solving this for <math> v </math> gives		Solving this for <math> v </math> gives

Richard.Udall: /* Computational Modelling */

2019-07-25T20:12:29Z

Computational Modelling

← Older revision		Revision as of 16:12, 25 July 2019
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	===Computational Modelling===		===Computational Modelling===
	Using the same computational techniques discussed in [[Fundamentals of Iterative Prediction with Varying Force]] and utilized in [[Simple Harmonic Motion]] and [[Iterative Prediction of Spring-Mass System]], it is simply necessary to define and input the newly defined force of air resistance. This is done so [https://colab.research.google.com/drive/1617NfftFpRj7BiZZFJZDI731MHC-J_q4#scrollTo=OS2_0AR6gW81 here] using numpy, and may also be done with VPython.		Using the same computational techniques discussed in [[Fundamentals of Iterative Prediction with Varying Force]] and utilized in [[Simple Harmonic Motion]] and [[Iterative Prediction of Spring-Mass System]], it is simply necessary to define and input the newly defined force of air resistance. This is done so [https://colab.research.google.com/drive/1617NfftFpRj7BiZZFJZDI731MHC-J_q4#scrollTo=OS2_0AR6gW81 here] using numpy, and may also be done with VPython.

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	===A Graphical Interpretation===		===A Graphical Interpretation===

Richard.Udall at 20:08, 25 July 2019

2019-07-25T20:08:23Z

← Older revision		Revision as of 16:08, 25 July 2019
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	~~claimed~~ by cshimkus3		'''Claimed by cshimkus3'''



			Because air resistance acts to oppose the movement of an object, and grows stronger the faster the object is moving, the object will eventually reach an equilibrium in which the force of air resistance is exactly equal and opposite to the force of gravity, so that there is no net force on the object. The speed at which this occurs can be computed algebraically, while the transitory stage as the object approaches this velocity requires (when working within the scope of this course) the use of computational methods.

	==Main Idea==		==Main Idea==

	~~===Mathematical Model===~~
	In [[Projectile Motion]], we considered the motion of an object under the influence of a constant gravitational force <math> g = 9.8 \; m/s^2 </math>, an approximation which is essentially accurate on the Earth's surface (the more accurate understanding, provided by Newton, may be found in [[Gravitational Force]]). However, we did not take into account a very important factor, because in everyday life, objects in motion '' do not '' stay in motion: this is because they are feeling the effects of air resistance (and, if they are in contact with other objects, friction). If, on the other hand, and object falls in a vacuum, it can be observed to have the same acceleration regardless of its mass or size. In the following video, a feather and a ball bearing are dropped inside a vacuum, and one may observe that they fall at exactly the same rate. (Click on the picture)		In [[Projectile Motion]], we considered the motion of an object under the influence of a constant gravitational force <math> g = 9.8 \; m/s^2 </math>, an approximation which is essentially accurate on the Earth's surface (the more accurate understanding, provided by Newton, may be found in [[Gravitational Force]]). However, we did not take into account a very important factor, because in everyday life, objects in motion '' do not '' stay in motion: this is because they are feeling the effects of air resistance (and, if they are in contact with other objects, friction). If, on the other hand, and object falls in a vacuum, it can be observed to have the same acceleration regardless of its mass or size. In the following video, a feather and a ball bearing are dropped inside a vacuum, and one may observe that they fall at exactly the same rate. (Click on the picture)

	[[File:Ballfeather.jpg \|link=https://www.youtube.com/watch?v=_XJcZ-KoL9o ]]		[[File:Ballfeather.jpg \|link=https://www.youtube.com/watch?v=_XJcZ-KoL9o ]]

			===Mathematical Model===

	The friction due to air is a non-constant force on a falling object, and is determined by a number of factors. The force of air on a falling object is defined as follows<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html </ref>:		The friction due to air is a non-constant force on a falling object, and is determined by a number of factors. The force of air on a falling object is defined as follows<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html </ref>:

Richard.Udall: /* History */

2019-06-26T17:12:52Z

History

← Older revision		Revision as of 13:12, 26 June 2019
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	==History==		==History==
			Understanding air resistance was a matter long complicated by its ubiquity. Aristotle recognized the presence of air and identified the presence of resistance, and Archimedes connected it to his knowledge of other fluids
			<ref> https://www.centennialofflight.net/essay/Theories_of_Flight/early_aero/TH3.htm </ref>, but neither effectively quantified it. Leonardo Da Vinci made some interesting developments, but his work was largely ignored, and so the next substantial improvement in understanding came with Galileo, who recognized the dependence of drag upon the density of the fluid. Next, Edme Mariotte and Christiaan Huygens separately determined the quadratic dependence on velocity, while Newton derived the dependence on surface area. The coefficient <math> C </math>, which incorporates the geometry of objects, is dependent on many factors in the fluid flow, and remains difficult to compute for complex objects or extreme conditions to this day <ref> https://www.grc.nasa.gov/www/k-12/airplane/drageq.html </ref>, due to the complexity of turbulent flows and other non-linear phenomena.



	~~The study of free fall began many centuries ago~~ by the ~~experiments~~ of ~~Aristotle~~ and ~~Galileo. They both monitored~~ the ~~motion~~ of ~~falling objects~~ and ~~Aristotle noted that if a feather and a hammer are dropped from the same height~~, ~~the hammer will reach the ground first~~. ~~Galileo~~, ~~however~~, ~~noted that if the hammer~~ and ~~feather had similar shapes, they would reach the ground at approximately~~ the ~~same time. He hypothesized that~~ in the ~~absence~~ of ~~air resistance, all objects falling from~~ the ~~same height will reach the ground at~~ the ~~same time~~. ~~Many centuries later~~, ~~when it became possible for his theory to be tested in a vacuum~~, ~~he was proved to be correct~~. ~~At this point~~, ~~physicists knew that it was air resistance and not mass that was~~ the ~~factor affecting the speed~~ of ~~a free fall. Further experiments were performed to determined~~ the ~~relationship between an objects shape~~ and ~~size and its terminal velocity. It was found that~~ objects ~~with a larger surface area perpendicular~~ to ~~free fall will be exposed to more air force than an object with a smaller surface areas~~. ~~From these experiments and relationships~~, ~~the equation for force~~ due to ~~air~~ and ~~terminal velocity were developed.~~

	~~[[File:Galileo-constant-gravity~~-~~pisa~~.~~png]]~~

	== See also ==		== See also ==

Richard.Udall: /* See also */

2019-06-26T16:54:22Z

See also

← Older revision		Revision as of 12:54, 26 June 2019
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	===Further reading===		===Further reading===
	~~[https://play.google.com/store/books/details/Wendy_MacDonald_Galileo_s_Leaning_Tower_Experiment?id=SzgVxrx3GZYC Galileo's Leaning Tower Experiment]~~

	~~[https://play~~.~~google.com/store/books/details/Georges_Voyiadjis_Materials_under_Extreme_Loadings?id=lE7izlz10j0C Materials under Extreme Loadings: Application to Penetration~~ and Impact]		Anderson, John David (1997). A History of Aerodynamics and its Impact on Flying machines.

	===External links===		===External links===
	[http://regentsprep.org/regents/physics/phys01/terminal/default.htm ~~The Physics Zone]~~		http://regentsprep.org/regents/physics/phys01/terminal/default.htm

	[http://www.britannica.com/science/terminal-velocity ~~Britannica Online]~~		http://www.britannica.com/science/terminal-velocity

	[https://www.grc.nasa.gov/www/k-12/airplane/termv.html ~~NASA]~~		https://www.grc.nasa.gov/www/k-12/airplane/termv.html

	==References==		==References==

Richard.Udall: /* History */

2019-06-26T16:42:42Z

History

← Older revision		Revision as of 12:42, 26 June 2019
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	==History==		==History==





	The study of free fall began many centuries ago by the experiments of Aristotle and Galileo. They both monitored the motion of falling objects and Aristotle noted that if a feather and a hammer are dropped from the same height, the hammer will reach the ground first. Galileo, however, noted that if the hammer and feather had similar shapes, they would reach the ground at approximately the same time. He hypothesized that in the absence of air resistance, all objects falling from the same height will reach the ground at the same time. Many centuries later, when it became possible for his theory to be tested in a vacuum, he was proved to be correct. At this point, physicists knew that it was air resistance and not mass that was the factor affecting the speed of a free fall. Further experiments were performed to determined the relationship between an objects shape and size and its terminal velocity. It was found that objects with a larger surface area perpendicular to free fall will be exposed to more air force than an object with a smaller surface areas. From these experiments and relationships, the equation for force due to air and terminal velocity were developed.		The study of free fall began many centuries ago by the experiments of Aristotle and Galileo. They both monitored the motion of falling objects and Aristotle noted that if a feather and a hammer are dropped from the same height, the hammer will reach the ground first. Galileo, however, noted that if the hammer and feather had similar shapes, they would reach the ground at approximately the same time. He hypothesized that in the absence of air resistance, all objects falling from the same height will reach the ground at the same time. Many centuries later, when it became possible for his theory to be tested in a vacuum, he was proved to be correct. At this point, physicists knew that it was air resistance and not mass that was the factor affecting the speed of a free fall. Further experiments were performed to determined the relationship between an objects shape and size and its terminal velocity. It was found that objects with a larger surface area perpendicular to free fall will be exposed to more air force than an object with a smaller surface areas. From these experiments and relationships, the equation for force due to air and terminal velocity were developed.

Richard.Udall: /* Computational Modelling */

2019-06-26T16:26:18Z

Computational Modelling

← Older revision		Revision as of 12:26, 26 June 2019
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	===Computational Modelling===		===Computational Modelling===
	Using the same computational techniques discussed in [[Fundamentals of Iterative Prediction with Varying Force]] and utilized in [[Simple Harmonic Motion]] and [[Iterative Prediction of Spring-Mass System]], it is simply necessary to define and input the newly defined force of air resistance. This is done so [https://colab.research.google.com/drive/1617NfftFpRj7BiZZFJZDI731MHC-J_q4#scrollTo=OS2_0AR6gW81 here] using numpy, and may also be done with VPython.		Using the same computational techniques discussed in [[Fundamentals of Iterative Prediction with Varying Force]] and utilized in [[Simple Harmonic Motion]] and [[Iterative Prediction of Spring-Mass System]], it is simply necessary to define and input the newly defined force of air resistance. This is done so [https://colab.research.google.com/drive/1617NfftFpRj7BiZZFJZDI731MHC-J_q4#scrollTo=OS2_0AR6gW81 here] using numpy, and may also be done with VPython.







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