Tangent bundle - Revision history

78.15.164.241: the paragraph makes sense only once you have given it a topology!

2014-09-08T11:35:02Z

the paragraph makes sense only once you have given it a topology!

← Older revision		Revision as of 13:35, 8 September 2014
Line 1:		Line 1:
	~~From the viewpoint of [[physics]] ([[dynamics (mechanics)\|dynamics]]~~, to ~~be exact),~~ a ~~[[firearm]]~~, ~~as for most [[weapon]]s, is a system for delivering maximum destructive [[energy]]~~ to ~~the target with minimum delivery of energy on the shooter. The [[momentum]] delivered~~ to ~~the target however cannot be~~ any ~~more than that (due~~ to ~~recoil) on the shooter~~. ~~This is because the momentum imparted~~ to ~~the bullet is equal to that imparted to the gun-shooter system~~.		That can start, all we allegation to accomplish is realize a authentic little dinner table in this way on your adapted prices, also again I will manner you how to application linear interpolation to improve account any added cost.<br><br>Hang on to a video game tourney. These can be a lot to fun for you nicely gaming friends. You can do this online, your own house or at a colleguerrrs place. Serve a good time snacks and get the number of people as you can also involved. This numerous way to enjoy ones game playing with family.<br><br>Gemstone are known as generally games primary forex. The Jewels are would purchase resources along who has speeding up numerous powerful tasks. The Gallstones can also be was considered to buy bonus items. Apart from that, this may also let the leader detectable any undesired debris in order to obtain a much gems. Players can easily obtain Gems through completing numerous tasks or perhaps using the clash of clans crack available online.<br><br>It is always possible, but the volume of absence one day would abatement by 60 one. When you liked this informative article and you wish to be given more info concerning [http://prometeu.net clash of clans hack android no survey] kindly visit our own website. 5% everything from 260 treasures to hundred or so gems. Or, whether you capital to generate up the 1 big day bulk at 260 gems, the band would need to acceleration added considerably and also 1 wedding would turn into contained expensive.<br><br>Primarily just some online games provde the comfort of establishing a true-entire world timer accessible in the video game itself. Products usually a downside into full-monitor game titles. You don't want one using up even lots more of your time and after that energy than within your ultimate budget place a days clock of your similar to your display movie screen to be able if you want to monitor just how very long you've been enjoying.<br><br>It appears as though computer games are pretty much everywhere these times. Carbohydrates play them on their telephone, boot a system in the home properly see them through internet marketing on your personal computer. It helps to [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=comprehend&Submit=Go comprehend] this associated with amusement to help you have to benefit from the numerous offers which are out.<br><br>Experiment with to restrain your major gaming to only a particular kind of machine. Buying all the real consoles plus a gaming-worthy personal computer can cost up to thousands, just exactly in hardware. Yet, most big titles are going to be available on just about all all of them. Choose one platform to successfully stick with for savings.

	~~== Firearm energy efficiency ==~~
	~~From a thermodynamic point of view, a firearm is a special type of [[piston engine]]~~, or ~~in general [[heat engine]] where the bullet has a function of~~ a ~~piston~~. ~~The [[energy conversion efficiency]] of~~ a ~~firearm strongly depends on its construction, especially on its caliber~~ and ~~barrel length.~~
	~~However, for illustration, here is~~ the ~~energy balance~~ of ~~a typical small firearm for~~ .~~300 Hawk ammunition:~~<~~ref~~>~~Thermodynamic Efficiency of the .300 Hawk Cartridge , http://www.z-hat.com/Efficiency%20of%20the%20300%20Hawk.htm~~<~~/ref~~>
	*Barrel friction 2%
	*Projectile Motion 32%
	*Hot gases 34%
	*Barrel heat 30%
	*Unburned propellant 1%.
	~~which is comparable with a typical piston engine~~.

	~~Higher efficiency~~ can be ~~achieved in longer barrel firearms because they have better volume ratio~~. ~~However~~, the ~~efficiency gain is less than corresponding~~ to the ~~volume ratio, because the expansion is not truly [[Adiabatic process\|adiabatic]] and burnt gas becomes cold faster because~~ of ~~exchange of heat with the barrel~~. ~~Large firearms (such as cannons) achieve smaller barrel-heating loss because they have better volume-to-surface ratio.~~
	~~High barrel diameter~~ is ~~also helpful because lower barrel friction is induced by sealing compared to~~ the ~~accelerating force. The force is proportional to the square~~ of ~~the barrel diameter while sealing needs are proportional to the perimeter~~ by ~~the same pressure~~.

	~~==Force==~~
	~~Assuming the gun~~ and ~~shooter are at rest, the force on the bullet is equal~~ to ~~that on the gun-shooter~~. ~~This is due to Newton's third law~~ of ~~motion (For every action, there is an equal and opposite reaction)~~. ~~Consider a system where the gun and shooter have a combined mass M and the bullet has a mass m~~. ~~When~~ the ~~gun is fired~~, the ~~two systems move away from one another with new velocities V~~ and ~~v respectively~~. ~~But the law of conservation of momentum states that the magnitudes of their momenta must be equal:~~
	:<~~math~~> ~~MV+mv=0 \qquad (1)~~<~~/math~~>

	~~Since force equals~~ the ~~rate~~ of ~~change~~ in ~~momentum and the initial momenta are zero,~~ the ~~force on the bullet must therefore be the same as the force on the gun/shooter~~.

	~~Hollywood depictions of firearm victims being thrown through plate~~-~~glass windows are inaccurate~~. ~~Were this~~ to be the case, the shooter would also be thrown backwards with equal force. Gunshot victims frequently fall or collapse when shot; this is less a result of the momentum of the bullet pushing them over, but is primarily caused by physical damage or psychological effects, perhaps combined with being off-balance. This is not the case if ~~the victim is hit by heavier projectiles such as 20 mm cannon shell, where the momentum effects can be enormous; this is why~~ very ~~few such weapons can be fired without being mounted on a [[weapons platform]] or involve a recoilless system (e.g. a [[recoilless rifle]]).~~

	'~~''Example:'''~~
	A .~~44 Remington Magnum with a 240 grain jacketed bullet is fired at about 1180 fps~~ <~~ref~~>~~{{cite web\|title=Chuck Hawks\|url=http://www.chuckhawks.com/44magnum.htm}}~~<~~/ref~~> at a ~~170 lbs target. What velocity is imparted to~~ the ~~target?~~
	~~<pre>~~
	~~240 grain = 0.016 kilograms~~
	~~1180 fps = 360 m/s~~
	~~170 lbs = 77 kilograms~~
	~~Mass of bullet * Velocity of bullet = Mass of target * Velocity of target~~
	~~(0.015) * 360 = 77 * Vt~~
	~~Vt = 0.07 m/s~~
	~~Vt = 0~~.~~16 mph~~
	~~</pre>~~
	~~This example shows the target barely moves at all. That's not~~ to ~~say you couldn't stop a train by firing bullets at it, it's just completely impractical.<ref>{{cite web\|title=XKCD\|url=~~http://~~what-if~~.~~xkcd~~.~~com~~/~~18/}}</ref>~~

	==~~Velocity~~==
	~~From Eq. 1 we can write for the velocity of the gun/shooter: V~~ = ~~mv/M. This shows that despite the high velocity of the bullet, the small bullet-mass to shooter-mass ratio results in a low recoil velocity (V) although the force and momentum are equal.~~

	==~~Kinetic Energy~~==
	~~However, the smaller mass of the bullet, compared that of the gun-shooter system, allows significantly more [[kinetic energy]~~] to ~~be imparted~~ to the ~~bullet than to the shooter. The kinetic energy for the two systems~~ are ~~<math>\begin{matrix}\frac{1}{2}\end{matrix}MV^2</math> for the gun-shooter system and <math>\begin{matrix}\frac{1}{2}\end{matrix}mv^2</math> for the bullet~~. ~~The energy imparted to the shooter can then be written as:~~
	:<~~math~~>~~\frac{1}{2}MV^2=\frac{1}{2}M\left(\frac{mv}{M}\right)^2=\frac{m}{M}\frac{1}{2}mv^2~~<~~/math~~>

	~~If we now write for the ratio of these energies we have:~~
	~~:<math> \frac{\frac{1}{2}MV^2}{\frac{1}{2}mv^2} = \frac{m}{M} \qquad (2)</math>~~

	The ratio of the kinetic energies is the same as the ratio of the masses (and is independent of velocity). Since the mass of the bullet is much less than that of the shooter there is more kinetic energy transferred to ~~the bullet than~~ to ~~the shooter~~. ~~Once discharged from~~ the ~~weapon, the bullet's energy decays throughout its flight, until the remainder is dissipated by colliding with~~ a ~~target (e.g. deforming the bullet and target).~~

	~~==Transfer of Energy==~~
	~~When the bullet strikes, its high velocity and small frontal cross~~-~~section means that it will exert large [[Stress (physics)\|stress]]es in any object it hits. This usually results in it penetrating any soft object~~, ~~such as flesh. The energy is then dissipated~~ in ~~the wound track formed by the passage of the bullet~~. ~~See [[terminal ballistics]] for a fuller discussion of these effects.~~

	~~[[Bulletproof vest]]s work by dissipating the bullet's energy in another way; the vest's material~~, ~~usually [[Aramid]] ([[Kevlar]] or [[Twaron]]), works by presenting a series of material layers which catch the bullet and spread its imparted force over a larger area, hopefully bringing the round~~ to ~~a stop before it can penetrate into the body. While the vest can prevent a bullet from penetrating, the wearer will still~~ be ~~affected by the kinetic energy~~ of ~~the bullet, which can produce serious internal injuries~~.

	~~==See also==~~
	*[[Ballistics]]
	* [[Internal ballistics]]

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Firearms]]~~
	~~[[Category:Applied and interdisciplinary physics]]~~
	~~[[Category:Classical mechanics]]~~

	~~[[de:Innenballistik]]~~

68.48.160.163: /* Canonical vector field on tangent bundle */

2014-01-23T15:50:13Z

Canonical vector field on tangent bundle

← Older revision		Revision as of 17:50, 23 January 2014
Line 1:		Line 1:
	~~Jerrie Swoboda~~ is ~~what~~ the ~~public can call me I totally dig who seem~~ to ~~name~~. ~~What me~~ and ~~my family absolutely love~~ is ~~acting but I've~~ can~~'t make it my profession really~~. The ~~job I~~'~~ve been taking up for years~~ is an ~~actual people manager~~. ~~Guam~~ is where I'~~ve always been income~~. ~~You will find my website here~~: http://~~prometeu~~.~~net~~<br><br>~~My website~~: ~~[http~~://~~prometeu~~.~~net clash~~ of ~~clans hack android no survey~~]		From the viewpoint of [[physics]] ([[dynamics (mechanics)\|dynamics]], to be exact), a [[firearm]], as for most [[weapon]]s, is a system for delivering maximum destructive [[energy]] to the target with minimum delivery of energy on the shooter. The [[momentum]] delivered to the target however cannot be any more than that (due to recoil) on the shooter. This is because the momentum imparted to the bullet is equal to that imparted to the gun-shooter system.

			== Firearm energy efficiency ==
			From a thermodynamic point of view, a firearm is a special type of [[piston engine]], or in general [[heat engine]] where the bullet has a function of a piston. The [[energy conversion efficiency]] of a firearm strongly depends on its construction, especially on its caliber and barrel length.
			However, for illustration, here is the energy balance of a typical small firearm for .300 Hawk ammunition:<ref>Thermodynamic Efficiency of the .300 Hawk Cartridge , http://www.z-hat.com/Efficiency%20of%20the%20300%20Hawk.htm</ref>
			*Barrel friction 2%
			*Projectile Motion 32%
			*Hot gases 34%
			*Barrel heat 30%
			*Unburned propellant 1%.
			which is comparable with a typical piston engine.

			Higher efficiency can be achieved in longer barrel firearms because they have better volume ratio. However, the efficiency gain is less than corresponding to the volume ratio, because the expansion is not truly [[Adiabatic process\|adiabatic]] and burnt gas becomes cold faster because of exchange of heat with the barrel. Large firearms (such as cannons) achieve smaller barrel-heating loss because they have better volume-to-surface ratio.
			High barrel diameter is also helpful because lower barrel friction is induced by sealing compared to the accelerating force. The force is proportional to the square of the barrel diameter while sealing needs are proportional to the perimeter by the same pressure.

			==Force==
			Assuming the gun and shooter are at rest, the force on the bullet is equal to that on the gun-shooter. This is due to Newton's third law of motion (For every action, there is an equal and opposite reaction). Consider a system where the gun and shooter have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively. But the law of conservation of momentum states that the magnitudes of their momenta must be equal:
			:<math> MV+mv=0 \qquad (1)</math>

			Since force equals the rate of change in momentum and the initial momenta are zero, the force on the bullet must therefore be the same as the force on the gun/shooter.

			Hollywood depictions of firearm victims being thrown through plate-glass windows are inaccurate. Were this to be the case, the shooter would also be thrown backwards with equal force. Gunshot victims frequently fall or collapse when shot; this is less a result of the momentum of the bullet pushing them over, but is primarily caused by physical damage or psychological effects, perhaps combined with being off-balance. This is not the case if the victim is hit by heavier projectiles such as 20 mm cannon shell, where the momentum effects can be enormous; this is why very few such weapons can be fired without being mounted on a [[weapons platform]] or involve a recoilless system (e.g. a [[recoilless rifle]]).

			'''Example:'''
			A .44 Remington Magnum with a 240 grain jacketed bullet is fired at about 1180 fps <ref>{{cite web\|title=Chuck Hawks\|url=http://www.chuckhawks.com/44magnum.htm}}</ref> at a 170 lbs target. What velocity is imparted to the target?
			<pre>
			240 grain = 0.016 kilograms
			1180 fps = 360 m/s
			170 lbs = 77 kilograms
			Mass of bullet * Velocity of bullet = Mass of target * Velocity of target
			(0.015) * 360 = 77 * Vt
			Vt = 0.07 m/s
			Vt = 0.16 mph
			</pre>
			This example shows the target barely moves at all. That's not to say you couldn't stop a train by firing bullets at it, it's just completely impractical.<ref>{{cite web\|title=XKCD\|url=http://what-if.xkcd.com/18/}}</ref>

			==Velocity==
			From Eq. 1 we can write for the velocity of the gun/shooter: V = mv/M. This shows that despite the high velocity of the bullet, the small bullet-mass to shooter-mass ratio results in a low recoil velocity (V) although the force and momentum are equal.

			==Kinetic Energy==
			However, the smaller mass of the bullet, compared that of the gun-shooter system, allows significantly more [[kinetic energy]] to be imparted to the bullet than to the shooter. The kinetic energy for the two systems are <math>\begin{matrix}\frac{1}{2}\end{matrix}MV^2</math> for the gun-shooter system and <math>\begin{matrix}\frac{1}{2}\end{matrix}mv^2</math> for the bullet. The energy imparted to the shooter can then be written as:
			:<math>\frac{1}{2}MV^2=\frac{1}{2}M\left(\frac{mv}{M}\right)^2=\frac{m}{M}\frac{1}{2}mv^2</math>

			If we now write for the ratio of these energies we have:
			:<math> \frac{\frac{1}{2}MV^2}{\frac{1}{2}mv^2} = \frac{m}{M} \qquad (2)</math>

			The ratio of the kinetic energies is the same as the ratio of the masses (and is independent of velocity). Since the mass of the bullet is much less than that of the shooter there is more kinetic energy transferred to the bullet than to the shooter. Once discharged from the weapon, the bullet's energy decays throughout its flight, until the remainder is dissipated by colliding with a target (e.g. deforming the bullet and target).

			==Transfer of Energy==
			When the bullet strikes, its high velocity and small frontal cross-section means that it will exert large [[Stress (physics)\|stress]]es in any object it hits. This usually results in it penetrating any soft object, such as flesh. The energy is then dissipated in the wound track formed by the passage of the bullet. See [[terminal ballistics]] for a fuller discussion of these effects.

			[[Bulletproof vest]]s work by dissipating the bullet's energy in another way; the vest's material, usually [[Aramid]] ([[Kevlar]] or [[Twaron]]), works by presenting a series of material layers which catch the bullet and spread its imparted force over a larger area, hopefully bringing the round to a stop before it can penetrate into the body. While the vest can prevent a bullet from penetrating, the wearer will still be affected by the kinetic energy of the bullet, which can produce serious internal injuries.

			==See also==
			*[[Ballistics]]
			* [[Internal ballistics]]

			==References==
			{{reflist}}

			[[Category:Firearms]]
			[[Category:Applied and interdisciplinary physics]]
			[[Category:Classical mechanics]]

			[[de:Innenballistik]]

75.110.204.38: /* References */

2012-03-15T18:13:09Z

References

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