View source for Newton's Second Law of Motion

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]]