Physics Book - User contributions [en]

Velocity

2017-04-02T15:17:54Z

Aazadi3:

Claimed and edited in Spring 2017 by Ali Azadi (aazadi3);

Explanation of work done by Ali: Some definitions and explanations more fleshed out; added more sample problems; reviewed prior content to ensure quality control

''Claimed by Stacey Nduati.''
edited by Christian Sewall
[[File:Whatisvelocity.gif|thumb|alt=Definition|What is velocity?]]

Velocity is the distance covered by an object in a specified direction over a time interval. In short, how fast something is moving, and what direction it is moving in. Velocity can be written as a vector, as it has both magnitude and direction. In contrast, speed only refers to how fast something is moving, has no direction, and is equivalent to the magnitude of the velocity (covered in section "Speed").

==Main Idea==
Velocity is the vector measure of the rate that the position of an object is changing divided by the time that change in position takes. This measure can be used in tandem with ideas such as The Momentum Principle to predict such values as position, momentum, and velocity after a specified time interval.Velocity has a large number of applications, such as use in identifying the perpendicular component of motion on an object, an object's kinetic energy, etc. Often times, a velocity can be constant, meaning that an object continues to travel in the same direction with the same magnitude and is often not acted on by any outside force (ex: a rocket travels in a straight line at a constant speed). Objects that are not in motion and stay in this state are also defined as having a constant velocity. When either the direction or magnitude of an object changes, generally due to an external force, velocity is no longer constant (ex: circular motion).

==A Mathematical Model==
The primary way that velocity can be modeled is
Average velocity can be calculated using the following equation:
:<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{r}}</math> is the vector change of position of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

<math>{\Delta\boldsymbol{r}}</math> can be found by subtracting the vector value of r<sub>final</sub> from the vector value of the original location, r<sub>initial</sub>, to obtain a resultant vector that represents the displacement between the two positions over the given time interval

The SI units for velocity are ''meters per second (m/s)''.

==A Computational Model==
This model defines an object and models its displacement arbitrarily with its mass in relation to time,

m=9
g=9.81
t=0
deltat=1
positionInitial=vector(0,0,0)
while t<6:
positionFinal=vector(0,m*g*t,0)
displacement=positionFinal-positionInitial
velocity=displacement/deltat
t=t+deltat
print (velocity ,"is velocity")

after t=6 is reached, the updated velocity is given.

This specific vPython example illustrates how a "while loop" may be used to update velocity, as velocity can be ever-changing as forces are applied.

==Example==

A car takes 3 hours to make a 230-mile trip from Point A to Point B.

{| border="1"
|+
! !! Hour 1 !! Hour 2 !! Hour 3
|-
! Velocity
| 80 mph north || 90 mph north || 60 mph north
|-
|}

There are two kinds of velocity in which one must consider: instantaneous velocity and average velocity.
[https://www.youtube.com/watch?v=Bxp0AWhs57g] does a good job explaining the difference between the two types of velocity

===Instantaneous Velocity===

Instantaneous velocity is the speed and direction of an object at a particular instant. Mathematically, it is the derivative of the position function at a specific point in time.

Given the example: Each hour, and each time point in every hour has a different instantaneous velocity.

===Average Velocity===

Average velocity is the net displacement of an object, divided by the total travel time. It is the average of all instantaneous velocities. It is important to note that as <math>{\Delta\mathit{t}}</math> gets very small, the average velocity approaches the instantaneous velocity.

Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph north.

==Acceleration==

Acceleration is the rate of change of velocity, divided by the change in time, modeled with with the following equation:
:<math>\boldsymbol{a} = \frac{\Delta\boldsymbol{v}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{v}}</math> is the change of velocity of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

The SI units for acceleration are ''meters per second squared (m/s/s)''. It is also a vector quantity.

Given the example: The acceleration from the 1st hour to the 2nd hour is 10 mph. This indicates a positive acceleration. The acceleration from the 2nd hour to the 3rd hour is -30 mph. This indicates a negative acceleration.

Colloquially acceleration is referred to as "speeding up" whilst "slowing down" is decelerating. Bear in mind that the direction does not have to change for deceleration to take place, it simply has to slow down.

<h2>Another Example</h2>
[[File:Velocity-time_graph_example.png]]

Based on what you know about velocity in relation to acceleration. During the time interval of 3-5 seconds is the object accelerating or decelerating? How about from 12-14 seconds? How do you know both of these answers?

Given the Example: From 3-5 seconds, knowing that acceleration is the derivative of velocity, it can be seen that the object is accelerating, as the graph has a positive slopes.From 12-14 seconds, the graph has an increasingly negative slope, signifying deceleration towards zero.

==Momentum==
Another application of velocity is within the realm of momentum and the Momentum Principle. momentum is defined as the mass of an object multiple by its vector velocity quantity. Like velocity momentum is a vector quantity. This quantity can be used in conjunction with change in time to see the amount of force applied on an object, and by extension its final location and velocity. This can be modeled iteratively through computer programs or be done in one calculation.

=Some Examples=

<h2> An Introductory Example </h2>
If a ball travels from location <2,4,6>m to <3,5,8>m in two seconds, what is its velocity?

Solution: :<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math>
Delta r: <3,5,8>m-<2,4,6>m and delta t is equal to 2s, so velocity is equal to the vector <1,1,2>m/2s, which is equal to <0.5,0.5,1> m/s

<h2> A More Difficult Example </h2>
A car is moving with a velocity of <26,87,12> m/s. If the initial location of the car is at <0,0,0>m and the final location of the car is at <39,130.5, 18> m, how many seconds did the car travel?

Assuming a constant velocity, delta r is equal to the final location of the car, since the car began at the origin. By dividing the delta r by the given velocity, a total time of two seconds of travel can be found.

<h2>A Final Example with Application of Momentum </h2>
If a van has a mass of 1200 kilograms, and it is traveling with a velocity of magnitude 38 m/s, what is its momentum?

Its momentum is 45,600 kg*m/s. This can be obtained by multiplying the mass by the magnitude of the velocity.

==Connectedness==
Velocity is a very simple yet interesting concept in the way that it can be applied to many different parts of physics from something as simple as displacement. Velocity's sheer versatility as a concept and the number of things that can be derived from it, which include acceleration, momentum, and by extension, force and mass. Also because it can be related to force, it can be used, in conjunction with other types of forces to determine many things about systems.

Velocity is also of critical importance in calculating kinetic energy (0.5*m*v^2). Through understanding both the relationship between kinetic energy and velocity, as well as the resulting relationship between kinetic energy and total energy, concepts such as potential spring, gravitational, and electric energies may also be related back to velocity. As Physics 1 deals primarily with motion and predicting future motion, velocity is an absolutely critical tool, as it can often be used to analyze changes of external forces and predict future movement.

Velocity relates to my career aspirations in a rather interesting way. Because I plan on trying to become a trauma doctor, its easy to see the difference between high and low velocity impacts of objects of the same mass. If a low mass object is accelerating at a high enough velocity, the ramifications of its impact with the body could be vastly different than an object with a low velocity.

An industrial application of velocity could be seen in cars and the limits of their engines. The limit to which a car engine can perform can be tested in various ways, one of them being velocity. This could be one reason why you don't see normal cars with speed past around 130, the engine simply can't take it. The knowledge of the limit of a car engine can be tested using velocity to help ensure a safe driving experience for many.

==See Also==
[http://www.physicsbook.gatech.edu/Relative_Velocity Relative Velocity]

[http://www.physicsbook.gatech.edu/Speed_and_Velocity Speed and Velocity]

[http://www.physicsbook.gatech.edu/Terminal_Speed Terminal Speed]

==References==

1. Chabay, Ruth W., and Bruce A. Sherwood. <i>Matter and Interactions</i>. Hoboken, NJ: Wiley, 2011. Print.

2. "Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.

3. <i>Velocity Expression</i>. Digital image. <i>Physics-Formulas</i>. N.p., n.d. Web. 29 Nov. 2015.

4. <i>Velocity vs Time Graph</i>. Digital image. <i>https://upload.wikimedia.org/wikipedia/commons/a/ae/Velocity-time_graph_example.png</i>. N.p., n.d. Web. 29 Nov. 2015.

==External links==

[http://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity The Physics Classroom: Speed and Velocity]

[http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html HyperPhysics: Average Velocity]

[[Category:Properties of Matter]]

Velocity

2017-04-02T14:50:05Z

Aazadi3:

Claimed and edited in Spring 2017 by Ali Azadi (aazadi3);
"Explanation of work done by Ali:

''Claimed by Stacey Nduati.''
edited by Christian Sewall
[[File:Whatisvelocity.gif|thumb|alt=Definition|What is velocity?]]

Velocity is the distance covered by an object in a specified direction over a time interval. In short, how fast something is moving, and what direction it is moving in. Velocity can be written as a vector, as it has both magnitude and direction. In contrast, speed only refers to how fast something is moving, has no direction, and is equivalent to the magnitude of the velocity (covered in section "Speed").

==Main Idea==
Velocity is the vector measure of the rate that the position of an object is changing divided by the time that change in position takes. This measure can be used in tandem with ideas such as The Momentum Principle to predict such values as position, momentum, and velocity after a specified time interval.

==A Mathematical Model==
The primary way that velocity can be modeled is
Average velocity can be calculated using the following equation:
:<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{r}}</math> is the vector change of position of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

<math>{\Delta\boldsymbol{r}}</math> can be found by subtracting the vector value of r<sub>final</sub> from the vector value of the original location, r<sub>initial</sub>, to obtain a resultant vector that represents the displacement between the two positions over the given time interval

The SI units for velocity are ''meters per second (m/s)''.

==A Computational Model==
This model defines an object and models is displacement arbitrarily with its mass in relation to time,

m=9
g=9.81
t=0
deltat=1
positionInitial=vector(0,0,0)
while t<6:
positionFinal=vector(0,m*g*t,0)
displacement=positionFinal-positionInitial
velocity=displacement/deltat
t=t+deltat
print (velocity ,"is velocity")

after t=6 is reached, the updated velocity is given.

==Example==

A car takes 3 hours to make a 230-mile trip from Point A to Point B.

{| border="1"
|+
! !! Hour 1 !! Hour 2 !! Hour 3
|-
! Velocity
| 80 mph north || 90 mph north || 60 mph north
|-
|}

There are two kinds of velocity in which one must consider: instantaneous velocity and average velocity.
[https://www.youtube.com/watch?v=Bxp0AWhs57g] does a good job explaining the difference between the two types of velocity

===Instantaneous Velocity===

Instantaneous velocity is the speed and direction of an object at a particular instant. Mathematically, it is the derivative of the position function at a specific point in time.

Given the example: Each hour, and each time point in every hour has a different instantaneous velocity.

===Average Velocity===

Average velocity is the net displacement of an object, divided by the total travel time. It is the average of all instantaneous velocities. It is important to note that as <math>{\Delta\mathit{t}}</math> gets very small, the average velocity approaches the instantaneous velocity.

Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph north.

==Acceleration==

Acceleration is the rate of change of velocity, divided by the change in time, modeled with with the following equation:
:<math>\boldsymbol{a} = \frac{\Delta\boldsymbol{v}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{v}}</math> is the change of velocity of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

The SI units for acceleration are ''meters per second squared (m/s/s)''. It is also a vector quantity.

Given the example: The acceleration from the 1st hour to the 2nd hour is 10 mph. This indicates a positive acceleration. The acceleration from the 2nd hour to the 3rd hour is -30 mph. This indicates a negative acceleration.

Colloquially acceleration is referred to as "speeding up" whilst "slowing down" is decelerating. Bear in mind that the direction does not have to change for deceleration to take place, it simply has to slow down.

<h2>Another Example</h2>
[[File:Velocity-time_graph_example.png]]

Based on what you know about velocity in relation to acceleration. During the time interval of 3-5 seconds is the object accelerating or decelerating? How about from 12-14 seconds? How do you know both of these answers?

Given the Example: From 3-5 seconds, knowing that acceleration is the derivative of velocity, it can be seen that the object is accelerating, as the graph has a positive slopes.From 12-14 seconds, the graph has an increasingly negative slope, signifying deceleration towards zero.

==Momentum==
Another application of velocity is within the realm of momentum and the Momentum Principle. momentum is defined as the mass of an object multiple by its vector velocity quantity. Like velocity momentum is a vector quantity. This quantity can be used in conjunction with change in time to see the amount of force applied on an object, and by extension its final location and velocity. This can be modeled iteratively through computer programs or be done in one calculation.

=Some Examples=

<h2> An Introductory Example </h2>
If a ball travels from location <2,4,6>m to <3,5,8>m in two seconds, what is its velocity?

Solution: :<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math>
Delta r: <3,5,8>m-<2,4,6>m and delta t is equal to 2s, so velocity is equal to the vector <1,1,2>m/2s, which is equal to <0.5,0.5,1> m/s

<h2>A Final Example</h2>
If a van has a mass of 1200 kilograms, and it is traveling with a velocity of magnitude 38 m/s, what is its momentum?

Its momentum is 45,600 kg*m/s. This can be obtained by multiplying the mass by the magnitude of the velocity.

==Connectedness==
Velocity is a very simple yet interesting concept in the way that it can be applied to many different parts of physics from something as simple as displacement. Velocity's sheer versatility as a concept and the number of things that can be derived from it, which include acceleration, momentum, and by extension, force and mass. Also because it can be related to force, it can be used, in conjunction with other types of forces to determine many things about systems.

Velocity relates to my career aspirations in a rather interesting way. Because I plan on trying to become a trauma doctor, its easy to see the difference between high and low velocity impacts of objects of the same mass. If a low mass object is accelerating at a high enough velocity, the ramifications of its impact with the body could be vastly different than an object with a low velocity.

An industrial application of velocity could be seen in cars and the limits of their engines. The limit to which a car engine can perform can be tested in various ways, one of them being velocity. This could be one reason why you don't see normal cars with speed past around 130, the engine simply can't take it. The knowledge of the limit of a car engine can be tested using velocity to help ensure a safe driving experience for many.

==See Also==
[http://www.physicsbook.gatech.edu/Relative_Velocity Relative Velocity]

[http://www.physicsbook.gatech.edu/Speed_and_Velocity Speed and Velocity]

[http://www.physicsbook.gatech.edu/Terminal_Speed Terminal Speed]

==References==

1. Chabay, Ruth W., and Bruce A. Sherwood. <i>Matter and Interactions</i>. Hoboken, NJ: Wiley, 2011. Print.

2. "Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.

3. <i>Velocity Expression</i>. Digital image. <i>Physics-Formulas</i>. N.p., n.d. Web. 29 Nov. 2015.

4. <i>Velocity vs Time Graph</i>. Digital image. <i>https://upload.wikimedia.org/wikipedia/commons/a/ae/Velocity-time_graph_example.png</i>. N.p., n.d. Web. 29 Nov. 2015.

==External links==

[http://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity The Physics Classroom: Speed and Velocity]

[http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html HyperPhysics: Average Velocity]

[[Category:Properties of Matter]]

Velocity

2017-04-02T14:49:00Z

Aazadi3:

Claimed and edited in Spring 2017 by Ali Azadi;
''Claimed by Stacey Nduati.''
edited by Christian Sewall
[[File:Whatisvelocity.gif|thumb|alt=Definition|What is velocity?]]

Velocity is the distance covered by an object in a specified direction over a time interval. In short, how fast something is moving, and what direction it is moving in. Velocity can be written as a vector, as it has both magnitude and direction. In contrast, speed only refers to how fast something is moving, has no direction, and is equivalent to the magnitude of the velocity (covered in section "Speed").

==Main Idea==
Velocity is the vector measure of the rate that the position of an object is changing divided by the time that change in position takes. This measure can be used in tandem with ideas such as The Momentum Principle to predict such values as position, momentum, and velocity after a specified time interval.

==A Mathematical Model==
The primary way that velocity can be modeled is
Average velocity can be calculated using the following equation:
:<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{r}}</math> is the vector change of position of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

<math>{\Delta\boldsymbol{r}}</math> can be found by subtracting the vector value of r<sub>final</sub> from the vector value of the original location, r<sub>initial</sub>, to obtain a resultant vector that represents the displacement between the two positions over the given time interval

The SI units for velocity are ''meters per second (m/s)''.

==A Computational Model==
This model defines an object and models is displacement arbitrarily with its mass in relation to time,

m=9
g=9.81
t=0
deltat=1
positionInitial=vector(0,0,0)
while t<6:
positionFinal=vector(0,m*g*t,0)
displacement=positionFinal-positionInitial
velocity=displacement/deltat
t=t+deltat
print (velocity ,"is velocity")

after t=6 is reached, the updated velocity is given.

==Example==

A car takes 3 hours to make a 230-mile trip from Point A to Point B.

{| border="1"
|+
! !! Hour 1 !! Hour 2 !! Hour 3
|-
! Velocity
| 80 mph north || 90 mph north || 60 mph north
|-
|}

There are two kinds of velocity in which one must consider: instantaneous velocity and average velocity.
[https://www.youtube.com/watch?v=Bxp0AWhs57g] does a good job explaining the difference between the two types of velocity

===Instantaneous Velocity===

Instantaneous velocity is the speed and direction of an object at a particular instant. Mathematically, it is the derivative of the position function at a specific point in time.

Given the example: Each hour, and each time point in every hour has a different instantaneous velocity.

===Average Velocity===

Average velocity is the net displacement of an object, divided by the total travel time. It is the average of all instantaneous velocities. It is important to note that as <math>{\Delta\mathit{t}}</math> gets very small, the average velocity approaches the instantaneous velocity.

Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph north.

==Acceleration==

Acceleration is the rate of change of velocity, divided by the change in time, modeled with with the following equation:
:<math>\boldsymbol{a} = \frac{\Delta\boldsymbol{v}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{v}}</math> is the change of velocity of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

The SI units for acceleration are ''meters per second squared (m/s/s)''. It is also a vector quantity.

Given the example: The acceleration from the 1st hour to the 2nd hour is 10 mph. This indicates a positive acceleration. The acceleration from the 2nd hour to the 3rd hour is -30 mph. This indicates a negative acceleration.

Colloquially acceleration is referred to as "speeding up" whilst "slowing down" is decelerating. Bear in mind that the direction does not have to change for deceleration to take place, it simply has to slow down.

<h2>Another Example</h2>
[[File:Velocity-time_graph_example.png]]

Based on what you know about velocity in relation to acceleration. During the time interval of 3-5 seconds is the object accelerating or decelerating? How about from 12-14 seconds? How do you know both of these answers?

Given the Example: From 3-5 seconds, knowing that acceleration is the derivative of velocity, it can be seen that the object is accelerating, as the graph has a positive slopes.From 12-14 seconds, the graph has an increasingly negative slope, signifying deceleration towards zero.

==Momentum==
Another application of velocity is within the realm of momentum and the Momentum Principle. momentum is defined as the mass of an object multiple by its vector velocity quantity. Like velocity momentum is a vector quantity. This quantity can be used in conjunction with change in time to see the amount of force applied on an object, and by extension its final location and velocity. This can be modeled iteratively through computer programs or be done in one calculation.

=Some Examples=

<h2> An Introductory Example </h2>
If a ball travels from location <2,4,6>m to <3,5,8>m in two seconds, what is its velocity?

Solution: :<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math>
Delta r: <3,5,8>m-<2,4,6>m and delta t is equal to 2s, so velocity is equal to the vector <1,1,2>m/2s, which is equal to <0.5,0.5,1> m/s

<h2>A Final Example</h2>
If a van has a mass of 1200 kilograms, and it is traveling with a velocity of magnitude 38 m/s, what is its momentum?

Its momentum is 45,600 kg*m/s. This can be obtained by multiplying the mass by the magnitude of the velocity.

==Connectedness==
Velocity is a very simple yet interesting concept in the way that it can be applied to many different parts of physics from something as simple as displacement. Velocity's sheer versatility as a concept and the number of things that can be derived from it, which include acceleration, momentum, and by extension, force and mass. Also because it can be related to force, it can be used, in conjunction with other types of forces to determine many things about systems.

Velocity relates to my career aspirations in a rather interesting way. Because I plan on trying to become a trauma doctor, its easy to see the difference between high and low velocity impacts of objects of the same mass. If a low mass object is accelerating at a high enough velocity, the ramifications of its impact with the body could be vastly different than an object with a low velocity.

An industrial application of velocity could be seen in cars and the limits of their engines. The limit to which a car engine can perform can be tested in various ways, one of them being velocity. This could be one reason why you don't see normal cars with speed past around 130, the engine simply can't take it. The knowledge of the limit of a car engine can be tested using velocity to help ensure a safe driving experience for many.

==See Also==
[http://www.physicsbook.gatech.edu/Relative_Velocity Relative Velocity]

[http://www.physicsbook.gatech.edu/Speed_and_Velocity Speed and Velocity]

[http://www.physicsbook.gatech.edu/Terminal_Speed Terminal Speed]

==References==

1. Chabay, Ruth W., and Bruce A. Sherwood. <i>Matter and Interactions</i>. Hoboken, NJ: Wiley, 2011. Print.

2. "Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.

3. <i>Velocity Expression</i>. Digital image. <i>Physics-Formulas</i>. N.p., n.d. Web. 29 Nov. 2015.

4. <i>Velocity vs Time Graph</i>. Digital image. <i>https://upload.wikimedia.org/wikipedia/commons/a/ae/Velocity-time_graph_example.png</i>. N.p., n.d. Web. 29 Nov. 2015.

==External links==

[http://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity The Physics Classroom: Speed and Velocity]

[http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html HyperPhysics: Average Velocity]

[[Category:Properties of Matter]]

Velocity

2017-04-02T14:48:39Z

Aazadi3:

Claimed and edited in Spring 2017 by Ali Azadi
''Claimed by Stacey Nduati.''
edited by Christian Sewall
[[File:Whatisvelocity.gif|thumb|alt=Definition|What is velocity?]]

Velocity is the distance covered by an object in a specified direction over a time interval. In short, how fast something is moving, and what direction it is moving in. Velocity can be written as a vector, as it has both magnitude and direction. In contrast, speed only refers to how fast something is moving, has no direction, and is equivalent to the magnitude of the velocity (covered in section "Speed").

==Main Idea==
Velocity is the vector measure of the rate that the position of an object is changing divided by the time that change in position takes. This measure can be used in tandem with ideas such as The Momentum Principle to predict such values as position, momentum, and velocity after a specified time interval.

==A Mathematical Model==
The primary way that velocity can be modeled is
Average velocity can be calculated using the following equation:
:<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{r}}</math> is the vector change of position of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

<math>{\Delta\boldsymbol{r}}</math> can be found by subtracting the vector value of r<sub>final</sub> from the vector value of the original location, r<sub>initial</sub>, to obtain a resultant vector that represents the displacement between the two positions over the given time interval

The SI units for velocity are ''meters per second (m/s)''.

==A Computational Model==
This model defines an object and models is displacement arbitrarily with its mass in relation to time,

m=9
g=9.81
t=0
deltat=1
positionInitial=vector(0,0,0)
while t<6:
positionFinal=vector(0,m*g*t,0)
displacement=positionFinal-positionInitial
velocity=displacement/deltat
t=t+deltat
print (velocity ,"is velocity")

after t=6 is reached, the updated velocity is given.

==Example==

A car takes 3 hours to make a 230-mile trip from Point A to Point B.

{| border="1"
|+
! !! Hour 1 !! Hour 2 !! Hour 3
|-
! Velocity
| 80 mph north || 90 mph north || 60 mph north
|-
|}

There are two kinds of velocity in which one must consider: instantaneous velocity and average velocity.
[https://www.youtube.com/watch?v=Bxp0AWhs57g] does a good job explaining the difference between the two types of velocity

===Instantaneous Velocity===

Instantaneous velocity is the speed and direction of an object at a particular instant. Mathematically, it is the derivative of the position function at a specific point in time.

Given the example: Each hour, and each time point in every hour has a different instantaneous velocity.

===Average Velocity===

Average velocity is the net displacement of an object, divided by the total travel time. It is the average of all instantaneous velocities. It is important to note that as <math>{\Delta\mathit{t}}</math> gets very small, the average velocity approaches the instantaneous velocity.

Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph north.

==Acceleration==

Acceleration is the rate of change of velocity, divided by the change in time, modeled with with the following equation:
:<math>\boldsymbol{a} = \frac{\Delta\boldsymbol{v}}{\Delta\mathit{t}}</math> ,
where <math>{\Delta\boldsymbol{v}}</math> is the change of velocity of the object and <math>{\Delta\mathit{t}}</math> is the change of time.

The SI units for acceleration are ''meters per second squared (m/s/s)''. It is also a vector quantity.

Given the example: The acceleration from the 1st hour to the 2nd hour is 10 mph. This indicates a positive acceleration. The acceleration from the 2nd hour to the 3rd hour is -30 mph. This indicates a negative acceleration.

Colloquially acceleration is referred to as "speeding up" whilst "slowing down" is decelerating. Bear in mind that the direction does not have to change for deceleration to take place, it simply has to slow down.

<h2>Another Example</h2>
[[File:Velocity-time_graph_example.png]]

Based on what you know about velocity in relation to acceleration. During the time interval of 3-5 seconds is the object accelerating or decelerating? How about from 12-14 seconds? How do you know both of these answers?

Given the Example: From 3-5 seconds, knowing that acceleration is the derivative of velocity, it can be seen that the object is accelerating, as the graph has a positive slopes.From 12-14 seconds, the graph has an increasingly negative slope, signifying deceleration towards zero.

==Momentum==
Another application of velocity is within the realm of momentum and the Momentum Principle. momentum is defined as the mass of an object multiple by its vector velocity quantity. Like velocity momentum is a vector quantity. This quantity can be used in conjunction with change in time to see the amount of force applied on an object, and by extension its final location and velocity. This can be modeled iteratively through computer programs or be done in one calculation.

=Some Examples=

<h2> An Introductory Example </h2>
If a ball travels from location <2,4,6>m to <3,5,8>m in two seconds, what is its velocity?

Solution: :<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}}</math>
Delta r: <3,5,8>m-<2,4,6>m and delta t is equal to 2s, so velocity is equal to the vector <1,1,2>m/2s, which is equal to <0.5,0.5,1> m/s

<h2>A Final Example</h2>
If a van has a mass of 1200 kilograms, and it is traveling with a velocity of magnitude 38 m/s, what is its momentum?

Its momentum is 45,600 kg*m/s. This can be obtained by multiplying the mass by the magnitude of the velocity.

==Connectedness==
Velocity is a very simple yet interesting concept in the way that it can be applied to many different parts of physics from something as simple as displacement. Velocity's sheer versatility as a concept and the number of things that can be derived from it, which include acceleration, momentum, and by extension, force and mass. Also because it can be related to force, it can be used, in conjunction with other types of forces to determine many things about systems.

Velocity relates to my career aspirations in a rather interesting way. Because I plan on trying to become a trauma doctor, its easy to see the difference between high and low velocity impacts of objects of the same mass. If a low mass object is accelerating at a high enough velocity, the ramifications of its impact with the body could be vastly different than an object with a low velocity.

An industrial application of velocity could be seen in cars and the limits of their engines. The limit to which a car engine can perform can be tested in various ways, one of them being velocity. This could be one reason why you don't see normal cars with speed past around 130, the engine simply can't take it. The knowledge of the limit of a car engine can be tested using velocity to help ensure a safe driving experience for many.

==See Also==
[http://www.physicsbook.gatech.edu/Relative_Velocity Relative Velocity]

[http://www.physicsbook.gatech.edu/Speed_and_Velocity Speed and Velocity]

[http://www.physicsbook.gatech.edu/Terminal_Speed Terminal Speed]

==References==

1. Chabay, Ruth W., and Bruce A. Sherwood. <i>Matter and Interactions</i>. Hoboken, NJ: Wiley, 2011. Print.

2. "Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.

3. <i>Velocity Expression</i>. Digital image. <i>Physics-Formulas</i>. N.p., n.d. Web. 29 Nov. 2015.

4. <i>Velocity vs Time Graph</i>. Digital image. <i>https://upload.wikimedia.org/wikipedia/commons/a/ae/Velocity-time_graph_example.png</i>. N.p., n.d. Web. 29 Nov. 2015.

==External links==

[http://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity The Physics Classroom: Speed and Velocity]

[http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html HyperPhysics: Average Velocity]

[[Category:Properties of Matter]]

Young's Modulus

2017-04-02T13:47:07Z

Aazadi3:

This page discusses Young's Modulus and examples of how it is used.
Pdorbala3

==The Main Idea==

Young's Modulus is a macroscopic property of a material that measures how stretchy a solid material is. It is independent of size or weight, and it will change depending on the material. The uses of Young's modulus extend to two main sets of relationships, macroscopic springs and microscopic springs. In the case of macroscopic springs, Young's modulus is a measure of the stretchiness of a solid material outside of considerations of size and shape. In microscopic strings, when a solid object is modeled as a system of balls (atoms) connected by springs (an image of which can be seen as the cover image of the physics textbook Matter and Interactions I 3rd Edition), the Young's modulus constant of the material can be used to determine the 'interatomic spring stiffness' constant Ksi of a material in order to determine the stiffness and stretchiness of interatomic bonds.

===A Mathematical Model===

The definition of Young's Modulus can be expressed as: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math> where <math>{F}_{T}</math> is equal to the tension force, <math>A</math> is equal to the cross sectional area, <math>ΔL</math> is equal to the change in length due to the tension force, and <math>L_o</math> is equal to the initial length of the material.

Young's Modulus can also be expressed as: <math>{Y = \frac{Ksi}{d}}</math> where Y is the Young's modulus of the material being examined, Ksi is the value that represents the interatomic bond stiffness (how much a bond between two atoms will stretch), and d is the distance from the center of one atom to the center of another atom.

===A Computational Model===

It's hard to demonstrate Young's Modulus through programming, but this photo does a great job of demonstrating the concept. A force causes a solid material to stretch by a constant certain amount. This relationship is named Young's Modulus and is independent of mass of the object, and varies based on material.
[[File:Youngs.jpeg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

'''Example 1.'''
A cylinder of wood has a stress of 800 and a strain of <math>8*10^-7</math>. What is Young's modulus for wood?

First we lay out the equation for the problem:

<math>Y = \frac{stress}{strain}</math>

We then plug in using the numbers given to us.

<math>Y = \frac{800}{8*10^-7}</math>

and so Y = 10^9 N/m^2

'''Example 2.'''

The Young's Modulus of Collagen in Bone is about 6 GPa [http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]. Given this, determine the force applied to a cylindrical segment of collagen of radius 1 cm and length 0.75 m to cause it to deform (stretch) 1 mm.

First, consider the equation of Young's modulus most useful for this problem:

<math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Substitute the appropriate values:

<math>6000000000 = \frac{\frac{{F}_{T}}{3.14*0.01^2}}{\frac{{0.001}}{0.75}}</math>

Solve for F:

<math>{F = 2.55*10^{10} Newtons}</math>

Does this seem reasonable?
Yes! because collagen that makes up bone is a very hard material, and does not stretch easily. Making bone stretch 1 mm longitudinally (using the bone as a vertical spring system) will take a lot of force.

===Middling===

'''Example 1.'''

A flan created by Dr. Schatz has a strawberry placed on it, stretching the flan from a length of 0.15 m to 0.2
m. The flan has a cross sectional area of .01. With the knowledge that flan has a Young’s
modulus of ~ 1.6e4 in tension, what force was used to stretch the flan?

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next we would fill in the equation for Young's Modulus: <math>{1.6e4 = \frac{\frac{{F}_{T}}{.01}}{\frac{{.05}}{.15}}}</math>

We can then fill in every thing that we know: <math>{16000 = 300*F_T}</math>

And so,<math>{F_T}</math> is equal to 53.3!

'''Example 2.'''

A man of weight 100 kg gets onto a bungee jump ride at a carnival. He is suspended in air by one rubber band (Young's Modulus of 0.01 GPa [http://www.engineeringtoolbox.com/young-modulus-d_417.html] of diameter 5 cm and original length of 10 m. Calculate the stretch of the band when the man reaches the bottom of the ride.

First, use the appropriate Young's Modulus equation:

<math>Y = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Then, substitute the appropriate values:

<math>{1e7 = \frac{{\frac{100*9.8}{3.14*0.05^2}}}{{\frac{ΔL}{10}}}}</math>

Solve:

<math>{ΔL=.125 m}</math>

===Difficult===

'''Example 1.'''

A new cylandrical flan is created by Dr. Schatz which has an orange placed on it which has a mass of .15 kg, compressing the flan a certain amount. Knowing that the initial length of the flan was .15 m and the flan has a diameter of .2 meters. With the knowledge that flan has a Young’s modulus of ~ 2e5 in tension, what length is the flan now?

First we need to write down the equation:

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next, let's solve for the unknowns:
Cross sectional area:

<math>{A} = pi*r^2</math>
<math>{A} = pi*.1^2</math>
<math>{A} = .0314 meters^2</math>

Force of the orange:

<math>{F}_{T} = m*g</math>
<math>{F}_{T} = .15*-9.8</math>
<math>{F}_{T} = -1.47 Newtons</math>

Next we would write out the equation for Youngs modulus: <math>{2e5 = \frac{\frac{-1.47}{.0314}}{\frac{{ΔL}}{.15}}}</math>

We can solve the equation for : <math>{-7/ΔL = 200000}</math>

And so,<math>{ΔL }</math> is equal to -3.5e-5! It was compressed 3.5e-5 meters!

'''Example 2.'''

Using the Young's modulus of Tungsten (<math>4*10^11</math>[http://www.engineeringtoolbox.com/young-modulus-d_417.html]) determine the interatomic "spring" stiffness of Tungsten.

First, find the center-to-center distance between 2 tungsten atoms.

<math>\frac{\frac{184 grams/mole}{6.022*10^23 atoms/mol}}{d^3}=19.25 g/cm^3</math> where d is the interatomic distance between Tungsten atoms. (19.25 g/cm^3 is the density of Tungsten[http://www.tungsten.com/materials/tungsten/]).

Solving, we get:

<math>d = 2.51e-8</math>

Using the appropriate formula:

<math>{Y = \frac{Ksi}{d}}</math>

<math>{4*10^11 = \frac{Ksi}{2.51e-8}}</math>

<math>{Ksi = 10040 N/m}</math>

==Connectedness==
#Young's modulus is connected to all solid material, and it highlights the slight impression given to everything showing that things do push down ever so slightly on stuff that seems stationary.
#My major is CS, so not a ton in physics directly applies to it, but Young's modulus is guaranteed to be in every physics simulation built which attempts to simulate the building integrity and usage of materials.
#Young's modulus is used all the time in civil engineering and it is often used to help determine structural integrity of certain materials when deciding on a building.
# Young's modulus has several biomedical applications in prosthetics and in human disease. It is used to determine the structural characteristics of prosthetic material used for implants. Young's modulus of tissues changes with aging and is being studied as a factor to evaluate mortality related to vascular stiffness from aging.

==History==

Young's Modulus was first developed in 1727 by the famous Leonhard Euler in Switzerland, but it was further expanded upon by Italian scientist Giordano Riccati in 1782. Finally, it was given a name by the British Scientist Thomas Young who finished work on it in the 1800s. It is used in order to discover the elasticity of solid materials and shows the stress per strain of a solid material.

== See also ==
[http://www.physicsbook.gatech.edu/Leonhard_Euler Leonhard Euler]

[http://www.physicsbook.gatech.edu/Thomas_Young Thomas Young]

===Further reading===

The VERY in-depth wiki page which goes for beyond applications in physics 1.[https://en.wikipedia.org/wiki/Young%27s_modulus]

===External links===

HyperPhysics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html] which is a great tool for just about any entry level physics.

==References==

Image: [http://s3.amazonaws.com/answer-board-image/48bb8d83-d333-4467-bfc0-de7c7c6d1c12.jpeg]

History: [https://en.wikipedia.org/wiki/Young%27s_modulus]

Young's Modulus Tables =
[http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]
[http://www.engineeringtoolbox.com/young-modulus-d_417.html]

[[Category:Contact Interactions]]

Young's Modulus

2017-04-02T13:46:42Z

Aazadi3:

This page discusses Young's Modulus and examples of how it is used.

==The Main Idea==

Young's Modulus is a macroscopic property of a material that measures how stretchy a solid material is. It is independent of size or weight, and it will change depending on the material. The uses of Young's modulus extend to two main sets of relationships, macroscopic springs and microscopic springs. In the case of macroscopic springs, Young's modulus is a measure of the stretchiness of a solid material outside of considerations of size and shape. In microscopic strings, when a solid object is modeled as a system of balls (atoms) connected by springs (an image of which can be seen as the cover image of the physics textbook Matter and Interactions I 3rd Edition), the Young's modulus constant of the material can be used to determine the 'interatomic spring stiffness' constant Ksi of a material in order to determine the stiffness and stretchiness of interatomic bonds.

===A Mathematical Model===

The definition of Young's Modulus can be expressed as: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math> where <math>{F}_{T}</math> is equal to the tension force, <math>A</math> is equal to the cross sectional area, <math>ΔL</math> is equal to the change in length due to the tension force, and <math>L_o</math> is equal to the initial length of the material.

Young's Modulus can also be expressed as: <math>{Y = \frac{Ksi}{d}}</math> where Y is the Young's modulus of the material being examined, Ksi is the value that represents the interatomic bond stiffness (how much a bond between two atoms will stretch), and d is the distance from the center of one atom to the center of another atom.

===A Computational Model===

It's hard to demonstrate Young's Modulus through programming, but this photo does a great job of demonstrating the concept. A force causes a solid material to stretch by a constant certain amount. This relationship is named Young's Modulus and is independent of mass of the object, and varies based on material.
[[File:Youngs.jpeg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

'''Example 1.'''
A cylinder of wood has a stress of 800 and a strain of <math>8*10^-7</math>. What is Young's modulus for wood?

First we lay out the equation for the problem:

<math>Y = \frac{stress}{strain}</math>

We then plug in using the numbers given to us.

<math>Y = \frac{800}{8*10^-7}</math>

and so Y = 10^9 N/m^2

'''Example 2.'''

The Young's Modulus of Collagen in Bone is about 6 GPa [http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]. Given this, determine the force applied to a cylindrical segment of collagen of radius 1 cm and length 0.75 m to cause it to deform (stretch) 1 mm.

First, consider the equation of Young's modulus most useful for this problem:

<math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Substitute the appropriate values:

<math>6000000000 = \frac{\frac{{F}_{T}}{3.14*0.01^2}}{\frac{{0.001}}{0.75}}</math>

Solve for F:

<math>{F = 2.55*10^{10} Newtons}</math>

Does this seem reasonable?
Yes! because collagen that makes up bone is a very hard material, and does not stretch easily. Making bone stretch 1 mm longitudinally (using the bone as a vertical spring system) will take a lot of force.

===Middling===

'''Example 1.'''

A flan created by Dr. Schatz has a strawberry placed on it, stretching the flan from a length of 0.15 m to 0.2
m. The flan has a cross sectional area of .01. With the knowledge that flan has a Young’s
modulus of ~ 1.6e4 in tension, what force was used to stretch the flan?

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next we would fill in the equation for Young's Modulus: <math>{1.6e4 = \frac{\frac{{F}_{T}}{.01}}{\frac{{.05}}{.15}}}</math>

We can then fill in every thing that we know: <math>{16000 = 300*F_T}</math>

And so,<math>{F_T}</math> is equal to 53.3!

'''Example 2.'''

A man of weight 100 kg gets onto a bungee jump ride at a carnival. He is suspended in air by one rubber band (Young's Modulus of 0.01 GPa [http://www.engineeringtoolbox.com/young-modulus-d_417.html] of diameter 5 cm and original length of 10 m. Calculate the stretch of the band when the man reaches the bottom of the ride.

First, use the appropriate Young's Modulus equation:

<math>Y = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Then, substitute the appropriate values:

<math>{1e7 = \frac{{\frac{100*9.8}{3.14*0.05^2}}}{{\frac{ΔL}{10}}}}</math>

Solve:

<math>{ΔL=.125 m}</math>

===Difficult===

'''Example 1.'''

A new cylandrical flan is created by Dr. Schatz which has an orange placed on it which has a mass of .15 kg, compressing the flan a certain amount. Knowing that the initial length of the flan was .15 m and the flan has a diameter of .2 meters. With the knowledge that flan has a Young’s modulus of ~ 2e5 in tension, what length is the flan now?

First we need to write down the equation:

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next, let's solve for the unknowns:
Cross sectional area:

<math>{A} = pi*r^2</math>
<math>{A} = pi*.1^2</math>
<math>{A} = .0314 meters^2</math>

Force of the orange:

<math>{F}_{T} = m*g</math>
<math>{F}_{T} = .15*-9.8</math>
<math>{F}_{T} = -1.47 Newtons</math>

Next we would write out the equation for Youngs modulus: <math>{2e5 = \frac{\frac{-1.47}{.0314}}{\frac{{ΔL}}{.15}}}</math>

We can solve the equation for : <math>{-7/ΔL = 200000}</math>

And so,<math>{ΔL }</math> is equal to -3.5e-5! It was compressed 3.5e-5 meters!

'''Example 2.'''

Using the Young's modulus of Tungsten (<math>4*10^11</math>[http://www.engineeringtoolbox.com/young-modulus-d_417.html]) determine the interatomic "spring" stiffness of Tungsten.

First, find the center-to-center distance between 2 tungsten atoms.

<math>\frac{\frac{184 grams/mole}{6.022*10^23 atoms/mol}}{d^3}=19.25 g/cm^3</math> where d is the interatomic distance between Tungsten atoms. (19.25 g/cm^3 is the density of Tungsten[http://www.tungsten.com/materials/tungsten/]).

Solving, we get:

<math>d = 2.51e-8</math>

Using the appropriate formula:

<math>{Y = \frac{Ksi}{d}}</math>

<math>{4*10^11 = \frac{Ksi}{2.51e-8}}</math>

<math>{Ksi = 10040 N/m}</math>

==Connectedness==
#Young's modulus is connected to all solid material, and it highlights the slight impression given to everything showing that things do push down ever so slightly on stuff that seems stationary.
#My major is CS, so not a ton in physics directly applies to it, but Young's modulus is guaranteed to be in every physics simulation built which attempts to simulate the building integrity and usage of materials.
#Young's modulus is used all the time in civil engineering and it is often used to help determine structural integrity of certain materials when deciding on a building.
# Young's modulus has several biomedical applications in prosthetics and in human disease. It is used to determine the structural characteristics of prosthetic material used for implants. Young's modulus of tissues changes with aging and is being studied as a factor to evaluate mortality related to vascular stiffness from aging.

==History==

Young's Modulus was first developed in 1727 by the famous Leonhard Euler in Switzerland, but it was further expanded upon by Italian scientist Giordano Riccati in 1782. Finally, it was given a name by the British Scientist Thomas Young who finished work on it in the 1800s. It is used in order to discover the elasticity of solid materials and shows the stress per strain of a solid material.

== See also ==
[http://www.physicsbook.gatech.edu/Leonhard_Euler Leonhard Euler]

[http://www.physicsbook.gatech.edu/Thomas_Young Thomas Young]

===Further reading===

The VERY in-depth wiki page which goes for beyond applications in physics 1.[https://en.wikipedia.org/wiki/Young%27s_modulus]

===External links===

HyperPhysics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html] which is a great tool for just about any entry level physics.

==References==

Image: [http://s3.amazonaws.com/answer-board-image/48bb8d83-d333-4467-bfc0-de7c7c6d1c12.jpeg]

History: [https://en.wikipedia.org/wiki/Young%27s_modulus]

Young's Modulus Tables =
[http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]
[http://www.engineeringtoolbox.com/young-modulus-d_417.html]

[[Category:Contact Interactions]]

Young's Modulus

2017-04-02T13:37:11Z

Aazadi3:

This page discusses Young's Modulus and examples of how it is used.

In 2017: Claimed by Ali Azadi (aazadi3)

==The Main Idea==

Young's Modulus is a macroscopic property of a material that measures how stretchy a solid material is. It is independent of size or weight, and it will change depending on the material. The uses of Young's modulus extend to two main sets of relationships, macroscopic springs and microscopic springs. In the case of macroscopic springs, Young's modulus is a measure of the stretchiness of a solid material outside of considerations of size and shape. In microscopic strings, when a solid object is modeled as a system of balls (atoms) connected by springs (an image of which can be seen as the cover image of the physics textbook Matter and Interactions I 3rd Edition), the Young's modulus constant of the material can be used to determine the 'interatomic spring stiffness' constant Ksi of a material in order to determine the stiffness and stretchiness of interatomic bonds.

===A Mathematical Model===

The definition of Young's Modulus can be expressed as: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math> where <math>{F}_{T}</math> is equal to the tension force, <math>A</math> is equal to the cross sectional area, <math>ΔL</math> is equal to the change in length due to the tension force, and <math>L_o</math> is equal to the initial length of the material.

Young's Modulus can also be expressed as: <math>{Y = \frac{Ksi}{d}}</math> where Y is the Young's modulus of the material being examined, Ksi is the value that represents the interatomic bond stiffness (how much a bond between two atoms will stretch), and d is the distance from the center of one atom to the center of another atom.

===A Computational Model===

It's hard to demonstrate Young's Modulus through programming, but this photo does a great job of demonstrating the concept. A force causes a solid material to stretch by a constant certain amount. This relationship is named Young's Modulus and is independent of mass of the object, and varies based on material.
[[File:Youngs.jpeg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

'''Example 1.'''
A cylinder of wood has a stress of 800 and a strain of <math>8*10^-7</math>. What is Young's modulus for wood?

First we lay out the equation for the problem:

<math>Y = \frac{stress}{strain}</math>

We then plug in using the numbers given to us.

<math>Y = \frac{800}{8*10^-7}</math>

and so Y = 10^9 N/m^2

'''Example 2.'''

The Young's Modulus of Collagen in Bone is about 6 GPa [http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]. Given this, determine the force applied to a cylindrical segment of collagen of radius 1 cm and length 0.75 m to cause it to deform (stretch) 1 mm.

First, consider the equation of Young's modulus most useful for this problem:

<math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Substitute the appropriate values:

<math>6000000000 = \frac{\frac{{F}_{T}}{3.14*0.01^2}}{\frac{{0.001}}{0.75}}</math>

Solve for F:

<math>{F = 2.55*10^{10} Newtons}</math>

Does this seem reasonable?
Yes! because collagen that makes up bone is a very hard material, and does not stretch easily. Making bone stretch 1 mm longitudinally (using the bone as a vertical spring system) will take a lot of force.

===Middling===

'''Example 1.'''

A flan created by Dr. Schatz has a strawberry placed on it, stretching the flan from a length of 0.15 m to 0.2
m. The flan has a cross sectional area of .01. With the knowledge that flan has a Young’s
modulus of ~ 1.6e4 in tension, what force was used to stretch the flan?

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next we would fill in the equation for Young's Modulus: <math>{1.6e4 = \frac{\frac{{F}_{T}}{.01}}{\frac{{.05}}{.15}}}</math>

We can then fill in every thing that we know: <math>{16000 = 300*F_T}</math>

And so,<math>{F_T}</math> is equal to 53.3!

'''Example 2.'''

A man of weight 100 kg gets onto a bungee jump ride at a carnival. He is suspended in air by one rubber band (Young's Modulus of 0.01 GPa [http://www.engineeringtoolbox.com/young-modulus-d_417.html] of diameter 5 cm and original length of 10 m. Calculate the stretch of the band when the man reaches the bottom of the ride.

First, use the appropriate Young's Modulus equation:

<math>Y = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Then, substitute the appropriate values:

<math>{1e7 = \frac{{\frac{100*9.8}{3.14*0.05^2}}}{{\frac{ΔL}{10}}}}</math>

Solve:

<math>{ΔL=.125 m}</math>

===Difficult===

'''Example 1.'''

A new cylandrical flan is created by Dr. Schatz which has an orange placed on it which has a mass of .15 kg, compressing the flan a certain amount. Knowing that the initial length of the flan was .15 m and the flan has a diameter of .2 meters. With the knowledge that flan has a Young’s modulus of ~ 2e5 in tension, what length is the flan now?

First we need to write down the equation:

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next, let's solve for the unknowns:
Cross sectional area:

<math>{A} = pi*r^2</math>
<math>{A} = pi*.1^2</math>
<math>{A} = .0314 meters^2</math>

Force of the orange:

<math>{F}_{T} = m*g</math>
<math>{F}_{T} = .15*-9.8</math>
<math>{F}_{T} = -1.47 Newtons</math>

Next we would write out the equation for Youngs modulus: <math>{2e5 = \frac{\frac{-1.47}{.0314}}{\frac{{ΔL}}{.15}}}</math>

We can solve the equation for : <math>{-7/ΔL = 200000}</math>

And so,<math>{ΔL }</math> is equal to -3.5e-5! It was compressed 3.5e-5 meters!

'''Example 2.'''

Using the Young's modulus of Tungsten (<math>4*10^11</math>[http://www.engineeringtoolbox.com/young-modulus-d_417.html]) determine the interatomic "spring" stiffness of Tungsten.

First, find the center-to-center distance between 2 tungsten atoms.

<math>\frac{\frac{184 grams/mole}{6.022*10^23 atoms/mol}}{d^3}=19.25 g/cm^3</math> where d is the interatomic distance between Tungsten atoms. (19.25 g/cm^3 is the density of Tungsten[http://www.tungsten.com/materials/tungsten/]).

Solving, we get:

<math>d = 2.51e-8</math>

Using the appropriate formula:

<math>{Y = \frac{Ksi}{d}}</math>

<math>{4*10^11 = \frac{Ksi}{2.51e-8}}</math>

<math>{Ksi = 10040 N/m}</math>

==Connectedness==
#Young's modulus is connected to all solid material, and it highlights the slight impression given to everything showing that things do push down ever so slightly on stuff that seems stationary.
#My major is CS, so not a ton in physics directly applies to it, but Young's modulus is guaranteed to be in every physics simulation built which attempts to simulate the building integrity and usage of materials.
#Young's modulus is used all the time in civil engineering and it is often used to help determine structural integrity of certain materials when deciding on a building.
# Young's modulus has several biomedical applications in prosthetics and in human disease. It is used to determine the structural characteristics of prosthetic material used for implants. Young's modulus of tissues changes with aging and is being studied as a factor to evaluate mortality related to vascular stiffness from aging.

==History==

Young's Modulus was first developed in 1727 by the famous Leonhard Euler in Switzerland, but it was further expanded upon by Italian scientist Giordano Riccati in 1782. Finally, it was given a name by the British Scientist Thomas Young who finished work on it in the 1800s. It is used in order to discover the elasticity of solid materials and shows the stress per strain of a solid material.

== See also ==
[http://www.physicsbook.gatech.edu/Leonhard_Euler Leonhard Euler]

[http://www.physicsbook.gatech.edu/Thomas_Young Thomas Young]

===Further reading===

The VERY in-depth wiki page which goes for beyond applications in physics 1.[https://en.wikipedia.org/wiki/Young%27s_modulus]

===External links===

HyperPhysics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html] which is a great tool for just about any entry level physics.

==References==

Image: [http://s3.amazonaws.com/answer-board-image/48bb8d83-d333-4467-bfc0-de7c7c6d1c12.jpeg]

History: [https://en.wikipedia.org/wiki/Young%27s_modulus]

Young's Modulus Tables =
[http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]
[http://www.engineeringtoolbox.com/young-modulus-d_417.html]

[[Category:Contact Interactions]]

Young's Modulus

2017-03-25T02:11:23Z

Aazadi3:

This page discusses Young's Modulus and examples of how it is used.

In 2017: Claimed by Ali Azadi (aazadi3)
I will be adding further applications of Young's Modulus and it's connectedness to intermolecular distances (as well as a few application problems) This will be done in the coming weekend (4/7/17). Please do not edit this page further (examples are being worked out and formatted before being finally added)
Claimed by Jlafiandra6

==The Main Idea==

Young's Modulus is a macroscopic property of a material that measures how stretchy a solid material is. It is independent of size or weight, and it will change depending on the material. The uses of Young's modulus extend to two main sets of relationships, macroscopic springs and microscopic springs. In the case of macroscopic springs, Young's modulus is a measure of the stretchiness of a solid material outside of considerations of size and shape. In microscopic strings, when a solid object is modeled as a system of balls (atoms) connected by springs (an image of which can be seen as the cover image of the physics textbook Matter and Interactions I 3rd Edition), the Young's modulus constant of the material can be used to determine the 'interatomic spring stiffness' constant Ksi of a material in order to determine the stiffness and stretchiness of interatomic bonds.

===A Mathematical Model===

The definition of Young's Modulus can be expressed as: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math> where <math>{F}_{T}</math> is equal to the tension force, <math>A</math> is equal to the cross sectional area, <math>ΔL</math> is equal to the change in length due to the tension force, and <math>L_o</math> is equal to the initial length of the material.

Young's Modulus can also be expressed as: <math>{Y = \frac{Ksi}{d}}</math> where Y is the Young's modulus of the material being examined, Ksi is the value that represents the interatomic bond stiffness (how much a bond between two atoms will stretch), and d is the distance from the center of one atom to the center of another atom.

===A Computational Model===

It's hard to demonstrate Young's Modulus through programming, but this photo does a great job of demonstrating the concept. A force causes a solid material to stretch by a constant certain amount. This relationship is named Young's Modulus and is independent of mass of the object, and varies based on material.
[[File:Youngs.jpeg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

'''Example 1.'''
A cylinder of wood has a stress of 800 and a strain of <math>8*10^-7</math>. What is Young's modulus for wood?

First we lay out the equation for the problem:

<math>Y = \frac{stress}{strain}</math>

We then plug in using the numbers given to us.

<math>Y = \frac{800}{8*10^-7}</math>

and so Y = 10^9 N/m^2

'''Example 2.'''

The Young's Modulus of Collagen in Bone is about 6 GPa [http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]. Given this, determine the force applied to a cylindrical segment of collagen of radius 1 cm and length 0.75 m to cause it to deform (stretch) 1 mm.

First, consider the equation of Young's modulus most useful for this problem:

<math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Substitute the appropriate values:

<math>6000000000 = \frac{\frac{{F}_{T}}{3.14*0.01^2}}{\frac{{0.001}}{0.75}}</math>

Solve for F:

<math>{F = 2.55*10^{10} Newtons}</math>

Does this seem reasonable?
Yes! because collagen that makes up bone is a very hard material, and does not stretch easily. Making bone stretch 1 mm longitudinally (using the bone as a vertical spring system) will take a lot of force.

===Middling===

'''Example 1.'''

A flan created by Dr. Schatz has a strawberry placed on it, stretching the flan from a length of 0.15 m to 0.2
m. The flan has a cross sectional area of .01. With the knowledge that flan has a Young’s
modulus of ~ 1.6e4 in tension, what force was used to stretch the flan?

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next we would fill in the equation for Young's Modulus: <math>{1.6e4 = \frac{\frac{{F}_{T}}{.01}}{\frac{{.05}}{.15}}}</math>

We can then fill in every thing that we know: <math>{16000 = 300*F_T}</math>

And so,<math>{F_T}</math> is equal to 53.3!

'''Example 2.'''

A man of weight 100 kg gets onto a bungee jump ride at a carnival. He is suspended in air by one rubber band (Young's Modulus of 0.01 GPa [http://www.engineeringtoolbox.com/young-modulus-d_417.html] of diameter 5 cm and original length of 10 m. Calculate the stretch of the band when the man reaches the bottom of the ride.

First, use the appropriate Young's Modulus equation:

<math>Y = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Then, substitute the appropriate values:

<math>{1e7 = \frac{{\frac{100*9.8}{3.14*0.05^2}}}{{\frac{ΔL}{10}}}}</math>

Solve:

<math>{ΔL=.125 m}</math>

===Difficult===

'''Example 1.'''

A new cylandrical flan is created by Dr. Schatz which has an orange placed on it which has a mass of .15 kg, compressing the flan a certain amount. Knowing that the initial length of the flan was .15 m and the flan has a diameter of .2 meters. With the knowledge that flan has a Young’s modulus of ~ 2e5 in tension, what length is the flan now?

First we need to write down the equation:

First we would write out the equation for Youngs modulus: <math>{Y = \frac{stress}{strain}} = \frac{\frac{{F}_{T}}{A}}{\frac{{ΔL}}{L_o}}</math>

Next, let's solve for the unknowns:
Cross sectional area:

<math>{A} = pi*r^2</math>
<math>{A} = pi*.1^2</math>
<math>{A} = .0314 meters^2</math>

Force of the orange:

<math>{F}_{T} = m*g</math>
<math>{F}_{T} = .15*-9.8</math>
<math>{F}_{T} = -1.47 Newtons</math>

Next we would write out the equation for Youngs modulus: <math>{2e5 = \frac{\frac{-1.47}{.0314}}{\frac{{ΔL}}{.15}}}</math>

We can solve the equation for : <math>{-7/ΔL = 200000}</math>

And so,<math>{ΔL }</math> is equal to -3.5e-5! It was compressed 3.5e-5 meters!

'''Example 2.'''

Using the Young's modulus of Tungsten (<math>4*10^11</math>[http://www.engineeringtoolbox.com/young-modulus-d_417.html]) determine the interatomic "spring" stiffness of Tungsten.

First, find the center-to-center distance between 2 tungsten atoms.

<math>\frac{\frac{184 grams/mole}{6.022*10^23 atoms/mol}}{d^3}=19.25 g/cm^3</math> where d is the interatomic distance between Tungsten atoms. (19.25 g/cm^3 is the density of Tungsten[http://www.tungsten.com/materials/tungsten/]).

Solving, we get:

<math>d = 2.51e-8</math>

Using the appropriate formula:

<math>{Y = \frac{Ksi}{d}}</math>

<math>{4*10^11 = \frac{Ksi}{2.51e-8}}</math>

<math>{Ksi = 10040 N/m}</math>

==Connectedness==
#Young's modulus is connected to all solid material, and it highlights the slight impression given to everything showing that things do push down ever so slightly on stuff that seems stationary.
#My major is CS, so not a ton in physics directly applies to it, but Young's modulus is guaranteed to be in every physics simulation built which attempts to simulate the building integrity and usage of materials.
#Young's modulus is used all the time in civil engineering and it is often used to help determine structural integrity of certain materials when deciding on a building.
# Young's modulus has several biomedical applications in prosthetics and in human disease. It is used to determine the structural characteristics of prosthetic material used for implants. Young's modulus of tissues changes with aging and is being studied as a factor to evaluate mortality related to vascular stiffness from aging.

==History==

Young's Modulus was first developed in 1727 by the famous Leonhard Euler in Switzerland, but it was further expanded upon by Italian scientist Giordano Riccati in 1782. Finally, it was given a name by the British Scientist Thomas Young who finished work on it in the 1800s. It is used in order to discover the elasticity of solid materials and shows the stress per strain of a solid material.

== See also ==
[http://www.physicsbook.gatech.edu/Leonhard_Euler Leonhard Euler]

[http://www.physicsbook.gatech.edu/Thomas_Young Thomas Young]

===Further reading===

The VERY in-depth wiki page which goes for beyond applications in physics 1.[https://en.wikipedia.org/wiki/Young%27s_modulus]

===External links===

HyperPhysics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html] which is a great tool for just about any entry level physics.

==References==

Image: [http://s3.amazonaws.com/answer-board-image/48bb8d83-d333-4467-bfc0-de7c7c6d1c12.jpeg]

History: [https://en.wikipedia.org/wiki/Young%27s_modulus]

Young's Modulus Tables =
[http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php]
[http://www.engineeringtoolbox.com/young-modulus-d_417.html]

[[Category:Contact Interactions]]