Physics Book - User contributions [en]

Newton's Second Law of Motion

2015-11-20T20:02:28Z

Inge14: /* Difficult */

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

Gravitational Extension:
<math>{\vec{F}_{gravity} = G}{\frac{M_{1}M_{2}}{r^2}}</math>

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
Question: A box is pushed on a frictionless surface with a force of 10N it accelerates to the right at 2m/s^2. What is the mass of the box?

Answer: Using the acceleration form of the second law, F=ma: it can be found that the box has a mass of 5kg.

===Middling===
Question: An 85kg skydiver is in free-fall. At some time later he experiences an air resistance force of 700N. Is he still accelerating and if so what is this acceleration?

Answer: To find out if he is still accelerating the net force on the skydiver needs to be found. After drawing a Free Body Diagram it can be seen that he is experiencing a gravitational force of 833N ((9.8m/s^2)*(85kg)) downwards and an air resistance force of 700N upwards. These are not in balance so he is still accelerating with a net force of 133N downwards. Using F=ma, it can be found that at that exact moment in time the skydiver's acceleration is 1.565m/s^2.
===Difficult===
Question:A child on a sled has been given a push so that she is moving up a hill. The hill is covered with icy snow and can be treated as frictionless. The child has a mass of 22.7 kg; the sled has a mass of 3.18 kg. What is the acceleration of the child as she moves up the incline? How far will she go before coming to a stop if her speed is 2 m/s when she starts at the bottom of the hill? She holds on tightly and so does not fall off the sled, and the hill makes an angle of 15.5 0 with the horizontal. Problem found from http://www.uwgb.edu/fenclh/problems/dynamics/2D/3/

Answer:[[File:NSL.JPG|500px]]

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T20:01:06Z

Inge14: /* Difficult */

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

Gravitational Extension:
<math>{\vec{F}_{gravity} = G}{\frac{M_{1}M_{2}}{r^2}}</math>

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
Question: A box is pushed on a frictionless surface with a force of 10N it accelerates to the right at 2m/s^2. What is the mass of the box?

Answer: Using the acceleration form of the second law, F=ma: it can be found that the box has a mass of 5kg.

===Middling===
Question: An 85kg skydiver is in free-fall. At some time later he experiences an air resistance force of 700N. Is he still accelerating and if so what is this acceleration?

Answer: To find out if he is still accelerating the net force on the skydiver needs to be found. After drawing a Free Body Diagram it can be seen that he is experiencing a gravitational force of 833N ((9.8m/s^2)*(85kg)) downwards and an air resistance force of 700N upwards. These are not in balance so he is still accelerating with a net force of 133N downwards. Using F=ma, it can be found that at that exact moment in time the skydiver's acceleration is 1.565m/s^2.
===Difficult===
Question:A child on a sled has been given a push so that she is moving up a hill. The hill is covered with icy snow and can be treated as frictionless. The child has a mass of 22.7 kg; the sled has a mass of 3.18 kg. What is the acceleration of the child as she moves up the incline? How far will she go before coming to a stop if her speed is 2 m/s when she starts at the bottom of the hill? She holds on tightly and so does not fall off the sled, and the hill makes an angle of 15.5 0 with the horizontal. Problem found from http://www.uwgb.edu/fenclh/problems/dynamics/2D/3/

Answer:[[File:NSL.JPG]]

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T20:00:29Z

Inge14: /* Difficult */

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

Gravitational Extension:
<math>{\vec{F}_{gravity} = G}{\frac{M_{1}M_{2}}{r^2}}</math>

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
Question: A box is pushed on a frictionless surface with a force of 10N it accelerates to the right at 2m/s^2. What is the mass of the box?

Answer: Using the acceleration form of the second law, F=ma: it can be found that the box has a mass of 5kg.

===Middling===
Question: An 85kg skydiver is in free-fall. At some time later he experiences an air resistance force of 700N. Is he still accelerating and if so what is this acceleration?

Answer: To find out if he is still accelerating the net force on the skydiver needs to be found. After drawing a Free Body Diagram it can be seen that he is experiencing a gravitational force of 833N ((9.8m/s^2)*(85kg)) downwards and an air resistance force of 700N upwards. These are not in balance so he is still accelerating with a net force of 133N downwards. Using F=ma, it can be found that at that exact moment in time the skydiver's acceleration is 1.565m/s^2.
===Difficult===
Question:A child on a sled has been given a push so that she is moving up a hill. The hill is covered with icy snow and can be treated as frictionless. The child has a mass of 22.7 kg; the sled has a mass of 3.18 kg. What is the acceleration of the child as she moves up the incline? How far will she go before coming to a stop if her speed is 2 m/s when she starts at the bottom of the hill? She holds on tightly and so does not fall off the sled, and the hill makes an angle of 15.5 0 with the horizontal. Problem found from http://www.uwgb.edu/fenclh/problems/dynamics/2D/3/

Answer:[[File:NSL.jpg]]

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

File:NSL.JPG

2015-11-20T19:59:56Z

Inge14: NSL

NSL

Newton's Second Law of Motion

2015-11-20T19:58:17Z

Inge14:

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

Gravitational Extension:
<math>{\vec{F}_{gravity} = G}{\frac{M_{1}M_{2}}{r^2}}</math>

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
Question: A box is pushed on a frictionless surface with a force of 10N it accelerates to the right at 2m/s^2. What is the mass of the box?

Answer: Using the acceleration form of the second law, F=ma: it can be found that the box has a mass of 5kg.

===Middling===
Question: An 85kg skydiver is in free-fall. At some time later he experiences an air resistance force of 700N. Is he still accelerating and if so what is this acceleration?

Answer: To find out if he is still accelerating the net force on the skydiver needs to be found. After drawing a Free Body Diagram it can be seen that he is experiencing a gravitational force of 833N ((9.8m/s^2)*(85kg)) downwards and an air resistance force of 700N upwards. These are not in balance so he is still accelerating with a net force of 133N downwards. Using F=ma, it can be found that at that exact moment in time the skydiver's acceleration is 1.565m/s^2.
===Difficult===
Question:A child on a sled has been given a push so that she is moving up a hill. The hill is covered with icy snow and can be treated as frictionless. The child has a mass of 22.7 kg; the sled has a mass of 3.18 kg. What is the acceleration of the child as she moves up the incline? How far will she go before coming to a stop if her speed is 2 m/s when she starts at the bottom of the hill? She holds on tightly and so does not fall off the sled, and the hill makes an angle of 15.5 0 with the horizontal. Problem found from http://www.uwgb.edu/fenclh/problems/dynamics/2D/3/

Answer:

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T19:52:24Z

Inge14:

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

Gravitational Extension:
<math>{\vec{F}_{gravity} = G}{\frac{M_{1}M_{2}}{r^2}}</math>

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
Question: A box is pushed on a frictionless surface with a force of 10N it accelerates to the right at 2m/s^2. What is the mass of the box?

Answer: Using the acceleration form of the second law, F=ma: it can be found that the box has a mass of 5kg.

===Middling===
Question: An 85kg skydiver is in free-fall. At some time later he experiences an air resistance force of 700N. Is he still accelerating and if so what is this acceleration?

Answer: To find out if he is still accelerating the net force on the skydiver needs to be found. After drawing a Free Body Diagram it can be seen that he is experiencing a gravitational force of 833N ((9.8m/s^2)*(85kg)) downwards and an air resistance force of 700N upwards. These are not in balance so he is still accelerating with a net force of 133N downwards. Using F=ma, it can be found that at that exact moment in time the skydiver's acceleration is 1.565m/s^2.
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T19:38:02Z

Inge14:

This topic covers Newton's Second Law of Motion.

==The Main Idea==

Newton's second law of motion states the explicit relationship between force on an object and the change in its momentum with respect to time.

===A Mathematical Model===
Momentum Form:
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Acceleration form:
<math>{\vec{F}_{net} = m}{\vec{a}}</math> where '''F_net''' is the net force on the system in Newtons, '''m''' is the mass of the system in Kg and '''a''' is the acceleration of the system in m/s^2.

===A Computational Model===

Glowscript Binary start program: http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/program/BinaryStar-VPython

vPython code from the above program:

GlowScript 1.1 VPython
# Binary star

scene.caption.append("""
Right button drag or Ctrl-drag to rotate "camera" to view scene.
To zoom, drag with middle button or Alt/Option depressed, or use scroll wheel.
On a two-button mouse, middle is left + right.
Touch screen: pinch/extend to zoom, swipe or two-finger rotate.""")

scene.forward = vector(0,-.3,-1)

G = 6.7e-11

giant = sphere(pos=vector(-1e11,0,0), radius=2e10, color=color.red,
make_trail=True, trail_type='points', interval=10, retain=50)
giant.mass = 2e30
giant.p = vector(0, 0, -1e4) * giant.mass

dwarf = sphere(pos=vector(1.5e11,0,0), radius=1e10, color=color.yellow,
make_trail=True, interval=10, retain=40)
dwarf.mass = 1e30
dwarf.p = -giant.p

dt = 1e5
while True:
rate(200)

r = dwarf.pos - giant.pos
F = G * giant.mass * dwarf.mass * norm(r) / mag2(r)
giant.p = giant.p + F*dt
dwarf.p = dwarf.p - F*dt
giant.pos = giant.pos + (giant.p/giant.mass) * dt
dwarf.pos = dwarf.pos + (dwarf.p/dwarf.mass) * dt

This Program uses the gravitational extension of Newton's second law to visually represent the orbits of a binary star system.

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T19:31:55Z

Inge14:

Newton's Second Law of Motion

2015-11-20T19:24:28Z

Inge14:

Newton's Second Law of Motion

2015-11-20T19:23:29Z

Inge14:

Newton's Second Law of Motion

2015-11-20T19:16:31Z

Inge14:

This topic covers Newton's Second Law of Motion.

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?

I am very interested in physical interactions on a celestial scale. From the inteactions between planets and there moons to how entire galaxies move, Newton's second law if vital to describing and understanding these interactions.

#How is it connected to your major?

As an Aerospace Engineer, mechanics as a whole is a vital tool when designing any device or form of machinery. Knowing how your work with interact with its surroundings is very necessary within all fields of engineering.

#Is there an interesting industrial application?

Every moving part in every machine ever built is bound by Newton's second law.

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T19:10:16Z

Inge14:

This topic covers Newton's Second Law of Motion.

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

'''Who:'''Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

'''What:'''Newton established a direct relationship between force and the second derivative of position (acceleration).

'''Where:'''Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

'''When:'''1687

'''Why:'''Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Newton's Second Law of Motion

2015-11-20T19:09:10Z

Inge14: Wiki page on Newton's Second Law

This topic covers Newton's Second Law of Motion.

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Who:Isaac Newton working off of Kepler's "Law of Constant Area" and the principle of Galilean Relativity (http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html).

What:Newton established a direct relationship between force and the second derivative of position (acceleration).

Where:Cambridge within his work titled: "Philosophiae Naturalis Principia Mathematica"

When:1687

Why:Because SCIENCE.

== See also ==

Sir Isaac Newton: http://www.physicsbook.gatech.edu/Sir_Isaac_Newton

Newton's First Law: http://www.physicsbook.gatech.edu/Newton%27s_First_Law_of_Motion

Mass: http://www.physicsbook.gatech.edu/Mass

===Further reading===

NASA's Explanation: https://www.grc.nasa.gov/www/K-12/airplane/newton2.html

Study.com's lesson: http://study.com/academy/lesson/newtons-second-law-of-motion-the-relationship-between-force-and-acceleration.html

===External links===

Mandatory Khan Academy link: https://www.khanacademy.org/science/physics/forces-newtons-laws/newtons-laws-of-motion/v/newton-s-second-law-of-motion

==References==

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Joshua Ingersoll November 20, 2015 <-- For Credit

[[Category:Interactions]]

Main Page

2015-11-20T18:42:29Z

Inge14:

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Catagories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[General Relativity]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Michael Faraday]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
* [[Inelastic Collision]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* Predicting Change in one dimension
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
* [[Right Hand Rule]]
* Predicting a Change in Rotation
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Spring Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Inelastic Collision]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
*[[Electric Force]]
*[[Polarization]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Faraday's Law]]
**[[Inductance]]
*[[Ampere-Maxwell Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]