Air Resistance - Revision history

Rcooper47 1: /* Main Idea */

2022-04-09T21:42:06Z

Main Idea

← Older revision		Revision as of 17:42, 9 April 2022
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	==Main Idea==		==Main Idea==
	[[File:Air resistance.jpg\|300px\|right]]		[[File:Air resistance.jpg\|300px\|right]]
	~~When~~ we ~~first look at physics principles, in specific~~ Newton’s Second Law and its affiliation to gravity and acceleration, we assume that an object in freefall will fall at a constant acceleration without any other forces acting upon it; however, this assumption is wrong. As an object moves through a medium(whether it be gas or liquid), forces that oppose the motion of the object come into play such as viscosity, drag, and air resistance; moreover, these principles form the basis of the field of physics centered around fluid dynamics, which examines this topic in great detail. Air Resistance is the force we see when we throw an object in the air and it is falling down, if we were to measure the acceleration at which an object is falling, we can see that the magnitude of the acceleration is decreasing due to a force acting in the opposite direction, known as air resistance. Air resistance is particularly important when examining objects in flight as to infer data on the motion of an object, we must properly be able to calculate the magnitude of the drag force in the form of air resistance.		Based on what we've learned about Newton’s Second Law and its affiliation to gravity and acceleration, we assume that an object in freefall will fall at a constant acceleration without any other forces acting upon it; however, this assumption is wrong. As an object moves through a medium(whether it be gas or liquid), forces that oppose the motion of the object come into play such as viscosity, drag, and air resistance; moreover, these principles form the basis of the field of physics centered around fluid dynamics, which examines this topic in great detail. Air Resistance is the force we see when we throw an object in the air and it is falling down, if we were to measure the acceleration at which an object is falling, we can see that the magnitude of the acceleration is decreasing due to a force acting in the opposite direction, known as air resistance. Air resistance is particularly important when examining objects in flight as to infer data on the motion of an object, we must properly be able to calculate the magnitude of the drag force in the form of air resistance.

	===Formulation===		===Formulation===

SidarthRajan: /* Difficult */

2020-11-16T04:15:33Z

Difficult

← Older revision		Revision as of 00:15, 16 November 2020
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	::::<math>F_{D} = \frac{1}{2}(2.3)((0.06)^2 \pi)(1.22)(1)^2</math>		::::<math>F_{D} = \frac{1}{2}(2.3)((0.06)^2 \pi)(1.22)(1)^2</math>
	::::<math>F_{D} = \frac{1}{2}(2.3)(0.01131)(1.22)(1)^2</math>		::::<math>F_{D} = \frac{1}{2}(2.3)(0.01131)(1.22)(1)^2</math>

			:::After calculating everything we can see that

			::::<math>F_{D} = 0.01587</math> N

	==Connectedness==		==Connectedness==

SidarthRajan: /* Difficult */

2020-11-16T04:13:46Z

Difficult

← Older revision		Revision as of 00:13, 16 November 2020
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	::::<math>\rho =</math> 1.22		::::<math>\rho =</math> 1.22
	::::<math>v =</math> 1.0		::::<math>v =</math> 1.0
	::::<math>A = (0.06)^2 ~~\times~~ \pi </math>		::::<math>A = (0.06)^2 \pi </math>
	::::<math>C_{D} =</math> ~~which is a non-dimensional constant that determines a relative~~ drag ~~depending on the shape of the object~~.		::::<math>C_{D} =</math> 2.3

			:::We now have everything we need to calculate the drag force

			::::<math>F_{D} = \frac{1}{2}C_{D} A \rho v^2</math>
			::::<math>F_{D} = \frac{1}{2}(2.3)((0.06)^2 \pi)(1.22)(1)^2</math>
			::::<math>F_{D} = \frac{1}{2}(2.3)(0.01131)(1.22)(1)^2</math>

	==Connectedness==		==Connectedness==

SidarthRajan: /* Difficult */

2020-11-16T04:10:40Z

Difficult

← Older revision		Revision as of 00:10, 16 November 2020
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	:'''b) What is the drag force at the end of the object's motion? Assume the drag constant is 2.3 and air has a density of 1.22 <math>\frac{kg}{m^3}</math>		:'''b) What is the drag force at the end of the object's motion? Assume the drag constant is 2.3 and air has a density of 1.22 <math>\frac{kg}{m^3}</math>

	::::<math>\rho =</math> ~~a measurement of the density of the medium~~		::::<math>\rho =</math> 1.22
	::::<math>v =</math> ~~the velocity of the object~~		::::<math>v =</math> 1.0
	::::<math>A =</math> ~~the cross-sectional area(looking for the area coming into contact with the air)~~		::::<math>A = (0.06)^2 \times \pi </math>
	::::<math>C_{D} =</math> which is a non-dimensional constant that determines a relative drag depending on the shape of the object.		::::<math>C_{D} =</math> which is a non-dimensional constant that determines a relative drag depending on the shape of the object.

SidarthRajan: /* Difficult */

2020-11-16T04:09:15Z

Difficult

← Older revision		Revision as of 00:09, 16 November 2020
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	:::<math>\Delta E_{a} = -(-0.03824) = 0.03824 \ J</math>		:::<math>\Delta E_{a} = -(-0.03824) = 0.03824 \ J</math>

	::~~'''~~We see the coffee filter lost <math>0.03824 \ J</math> of energy, and the air in contact with the coffee filter gained it.~~'''~~		::We see the coffee filter lost <math>0.03824 \ J</math> of energy, and the air in contact with the coffee filter gained it.

	:'''b) What is the drag force at the end of the object's motion? Assume the drag constant is 2.3.		:'''b) What is the drag force at the end of the object's motion? Assume the drag constant is 2.3 and air has a density of 1.22 <math>\frac{kg}{m^3}</math>

	::::<math>\rho =</math> a measurement of the density of the medium		::::<math>\rho =</math> a measurement of the density of the medium

SidarthRajan: /* Difficult */

2020-11-16T04:06:42Z

Difficult

← Older revision		Revision as of 00:06, 16 November 2020
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	===Difficult===		===Difficult===
	Sarah is doing an air resistance experiment in class. The experiment requires Sarah to drop a coffee filter from a height of 2 meters. Let's say that the mass of the coffee filter was 2.0 grams, and it reached the ground with a speed of 1.0 m/s.		Sarah is doing an air resistance experiment in class. The experiment requires Sarah to drop a coffee filter from a height of 2 meters. Let's say that the mass of the coffee filter was 2.0 grams, the radius of its base was 6 cm, and it reached the ground with a speed of 1.0 m/s.

	:'''a) How much energy did the air gain as the coffee filter floated down?		:'''a) How much energy did the air gain as the coffee filter floated down?
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	::'''We see the coffee filter lost <math>0.03824 \ J</math> of energy, and the air in contact with the coffee filter gained it.'''		::'''We see the coffee filter lost <math>0.03824 \ J</math> of energy, and the air in contact with the coffee filter gained it.'''

			:'''b) What is the drag force at the end of the object's motion? Assume the drag constant is 2.3.

			::::<math>\rho =</math> a measurement of the density of the medium
			::::<math>v =</math> the velocity of the object
			::::<math>A =</math> the cross-sectional area(looking for the area coming into contact with the air)
			::::<math>C_{D} =</math> which is a non-dimensional constant that determines a relative drag depending on the shape of the object.

	==Connectedness==		==Connectedness==

SidarthRajan: /* Connectedness */

2020-11-16T03:52:42Z

Connectedness

← Older revision		Revision as of 23:52, 15 November 2020
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	'''How is this topic connected to something that you are interested in?'''		'''How is this topic connected to something that you are interested in?'''

	*~~As an adventurous person, I have always been interested in skydiving.~~ Air resistance is a ~~huge~~ factor in ~~skydiving~~, as it ~~allows you to reach the ground safely just~~ with ~~a parachute. There are many factors in releasing a parachute~~ to ~~have the safest possible landing. When you release your parachute and how to control your parachute are very important in having a safe landing~~. ~~Also~~, ~~there~~ is ~~obviously a lot~~ of air resistance ~~in a parachute because~~ of the ~~large cross sectional area~~.		*Air resistance plays a big factor in sports, and physical activity. We can see that during sports such as football, rugby, and soccer when the ball is kicked upwards, it travels downwards with an amount of drag, which is important to take into consideration when playing these sports. Furthermore, the sport of ultimate frisbee is entirely based upon the principle of air resistance, as really good players know how to manipulate the air to cause the best throws and motion of the frisbee.

	*~~Another topic~~ that air resistance ~~plays a factor~~ in ~~is sports. A~~ specific ~~sport that air resistance impacts~~ is ~~tennis. Spin is very important~~ in ~~tennis~~, ~~because it allows~~ you ~~to control where the ball lands~~. ~~If there~~ is ~~topspin on a ball, the air resistance is less allowing the ball~~ to ~~come down faster. If there~~ is ~~backspin, the ball stays~~ in ~~the~~ air ~~longer~~, ~~being controlled by~~ the ~~air.~~		*We can also see that the concept of air resistance in specific its relation to the overall concept of drag, is present throughout the universe in many different forms, one of them being the drag you feel against water. We know that it is much harder to move underwater than it is in air, and that is due to the fluid mechanics behind the motion between both mediums, and the increased drag in water.

	*Moreover, the simulation of motions in animations are also very interesting. If you ignore the air resistance of the motion, ~~it will be absolutely very fake. Amazingly people have~~ the ~~sense to tell which scene is more actual and authentic. When you make an animation of snow flickers floating~~ in ~~the sky, it is important for you to precisely take air resistance forces into count~~.

	'''How is it connected to your major?'''		'''How is it connected to your major?'''

	*I am a ~~Biomolecular Engineering~~ major. ~~Although my major seems to have nothing related to air resistance, the topic can be generalized to many other resistance~~ forces~~. For example, we can apply the resistance force equation to water, and simulate~~ a ~~diver~~'s motion to ~~find~~ the ~~best fitted materials for diving suits~~. ~~Maybe~~ it is ~~also possible for us to develop some important first-aid machines or devices that can~~ be ~~easily carried through any kind~~ of ~~surrounding substances~~.		*I am a computer science major who is interested in speciation in artificial intelligence and computer vision. Dealing with forces involved in a drone's or vehicle's motion is exactly what I will be having to deal with in the future. Learning how drag force is dependent on the speed proves that it is constantly changing, and must constantly be updated and factored into calculations regardless of whether the motion is vertical or lateral.

	'''Is there an interesting industrial application?'''		'''Is there an interesting industrial application?'''

	*Air resistance has a lot of ~~application in speed sports~~. ~~Also~~, air resistance ~~plays a big factor~~ in ~~skydiving~~ and ~~anything with a parachute~~. ~~Lastly~~, the ~~aircraft industry factors in air resistance into all~~ of ~~their products, as this force~~ is ~~very important in takeoff, landing, and flight~~.		*Air resistance has a lot of applications throughout academia, entertainment, security, and many other things. Through academia, we can examine how air resistance impacts the motion of objects in freefall and we can see the magnitude that it has on an object's net speed. Moreoever, through the sports world, we can see how knowing how to control the amount of drag that will be on a ball is imperative towards reaching higher athletic goals.

	==History==		==History==

SidarthRajan at 02:48, 16 November 2020

2020-11-16T02:48:09Z

← Older revision		Revision as of 22:48, 15 November 2020
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	We have encountered the term of 'cross-sectional area' in many cases: for example, when you need to calculate the flux of a liquid flowing through a pipe, you need the cross-sectional area to determine the volume of the liquid flowing through. However, the 'cross-sectional area' here is different. We'd better see it as the 'frontal area': the area facing the direction of the object's movement.		We have encountered the term of 'cross-sectional area' in many cases: for example, when you need to calculate the flux of a liquid flowing through a pipe, you need the cross-sectional area to determine the volume of the liquid flowing through. However, the 'cross-sectional area' here is different. We'd better see it as the 'frontal area': the area facing the direction of the object's movement.

	It is easy to understand: we can relate this idea to the choice of the system and moving objects. For example, when a plane is flying forward with a speed <math>v</math> in the <math>+x</math> direction and the air is static, only the surface of the plane pointing in the <math>+x</math> direction is subject to the air resistance, since most air particles are colliding with that area with relatively high speed in the opposite direction.		It is easy to understand: we can relate this idea to the choice of the system and moving objects. For example, when a plane is flying forward with a speed <math>v</math> in the <math>+x</math> direction and the air is static, only the surface of the plane pointing in the <math>+x</math> direction is subject to the air resistance since most air particles are colliding with that area with relatively high speed in the opposite direction.

			Essentially, what we are describing buy the cross-sectional area is the portion of the surface area that is facing the direction of the object's motion, as this will be the area that has the most in contact with external mediums such as air. When we examine air resistance, we look at the area of the object that is facing the air. Conceptually speaking, we can see from the mathematical model that as the cross-sectional area increases the magnitude of the drag force also increases, this is due to the fact that there is more area of the object coming into contact with the specific medium.

			=====Skydiver/Parachute Example=====
			When we view skydivers, we can see that when they move downwards headfirst they tend to travel much faster than when they move stomach first. Why is this?

			When a skydiver is traveling headfirst, the cross-sectional area coming into contact with the air is simply the area on the skull, which is substantially smaller than the surface area of the anterior side of your body. Therefore since less area is coming into contact with the air, the drag force is much less, which causes a greater acceleration as opposed to one with a greater surface area.

			This also explains why parachutes open up with a wide surface area on the inside, as the entirety of the inside is coming into contact with the air, allowing for a large drag force, which causes the acceleration to fall greatly until one reaches terminal speed.

	====Drag Coefficient====		====Drag Coefficient====
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	===Computational Model===		===Computational Model===
	:[[https://trinket.io/glowscript/~~4eccc56a54~~]]		:[[https://trinket.io/glowscript/f95f56408b]]

	==Examples==		==Examples==

SidarthRajan: /* Main Idea */

2020-11-16T02:27:19Z

Main Idea

← Older revision		Revision as of 22:27, 15 November 2020
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	===Computational Model===		===Computational Model===
	:~~'''Insert Computational Model here'''~~		:[[https://trinket.io/glowscript/4eccc56a54]]

	==Examples==		==Examples==

SidarthRajan: /* Main Idea */

2020-11-16T01:50:06Z

Main Idea

← Older revision		Revision as of 21:50, 15 November 2020
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	::::<math>A =</math> the cross-sectional area(looking for the area coming into contact with the air)		::::<math>A =</math> the cross-sectional area(looking for the area coming into contact with the air)
	::::<math>C_{D} =</math> which is a non-dimensional constant that determines a relative drag depending on the shape of the object.		::::<math>C_{D} =</math> which is a non-dimensional constant that determines a relative drag depending on the shape of the object.


	===Mathematical Model===		===Mathematical Model===