Claimed by Blake Castleman 11/23/2018 (Work in Progress)

This page discusses the concept of friction and how it relates to both moving and static objects.

==The Main Idea==
Friction is caused by the interactions between the atoms that make up objects. When objects interact, the atoms that make up the objects also interact. Temperatures of interacting surfaces rise because of such interactions. Friction is a force that resists movement. Generally, friction makes it harder to move objects. There are two main types of friction that are covered in Physics 2211: Static Friction and Kinetic Friction. Static friction can be described as the friction acting on resting objects. Kinetic friction is the friction acting on objects in motion.

Frictional forces depend on a few factors: the normal force and the coefficient of friction.

In simple terms, the normal force <math> {F}_{N} </math> or <math> {N} </math> is the equivalent force between objects. For example, when an object of mass '''M''' is placed on a table, there is a gravitational force '''Mg''' on the table. If the table can support the object without collapsing, the table exerts an equivalent force '''Mg''' on the object. According to the momentum principle, since there is no change in momentum, the net force must be '''0'''. This is also apparent since there is no movement if the table can support the object.

::<math> {p}_{f} - {p}_{i} = {F}_{net}{dt} = 0 </math>

OR

::<math> {F}_{g} = {M}{g} </math>
::<math> {N} = {M}{g} </math>
::<math> {F}_{net} = {F}_{g} - {N} = {0} </math>

The coefficient of friction is usually specific to each object or material. The coefficient of static friction is denoted by <math>{μ}_{s}</math> and the coefficient of kinetic friction is denoted by <math>{μ}_{k}</math>

Static Friction:

::<math> {F}_{s} \le {μ}_{s}{N} </math>

Static friction is the frictional force that must be overcome to begin moving an object at rest. The static friction can be no more than the normal force multiplied by the coefficient of static friction. Therefore, the maximum static friction an object can have is <math> {μ}_{s}{N} </math>.

Kinetic Friction:

::<math> {F}_{k} = {μ}_{k}{N} </math>

Kinetic friction is the frictional force that exists between objects already at motion. It acts to oppose the movement of an object. Kinetic friction can be observed, for example, when a soccer ball is kicked across a field. The friction between the ball and the field will eventually bring the ball to a stop.

Interestingly, friction is also required for rolling motion. Without friction, objects would not be able to roll. This is true because friction results in torque acting on the object, causing the rolling motion. An example of this can be seen in cars that are stuck in a ditch or similar situations. If there is not enough friction between the car's wheels and the ground, the car's wheels will simply spin in place, and the car will not move.

===A Mathematical Model===

As stated above:

Static Friction:

::<math> {F}_{s} \le {μ}_{s}{N} </math>

Kinetic Friction:

::<math> {F}_{k} = {μ}_{k}{N} </math>

When attempting to solve problems relating to friction, one possible method of approach is to consider the net force acting on an object. If there is a force <math> {F}</math> pushing an object to the right, and a frictional force <math>{F}_{f}</math> opposing the movement, then the net force is <math> {F}_{net} = {F} - {F}_{f} </math>.

Another possible approach is by using the momentum principle <math> {p}_{f} - {p}_{i} = {F}_{net}{dt} </math>. The momentum principle can help solve problems where you need to account for time, net force, or change in momentum.

===A Computational Model===

[[File:Friction.gif]]

Link:
https://trinket.io/glowscript/76028c1809

Code:
def friction():
from __future__ import division
from visual import *
from visual.graph import *

mcart = 100
mew = vector(2.9,0,0)

track = box(pos=vector(0,-0.05,0), size=vector(20.0,0.05,0.10), color=color.white)
cart = box(pos=vector(-10,0.25,0), size=vector(.5,0.6,0.03), color=color.blue)
marker = box(pos = vector(2,0,0), size = vector(0,20,5), color = color.red)

cart.v=vector(2.4,0,0)
cart.p = mcart*cart.v
F = vector(90,0,0)
F2 = vector(-200,0,0)
F3 = (mcart * mew)
print(F3)

deltat = 0.01
t = 0

while t < 5.02:

if cart.pos.x < 2:
cart.v = cart.p / cart.m
Fnet = F
cart.p = cart.p + Fnet*deltat
cart.pos = cart.pos + (cart.p/mcart)*deltat

else:

cart.v = cart.p / cart.m
Fnet = F-F3
cart.p = cart.p + Fnet*deltat
cart.pos = cart.pos + (cart.p/mcart)*deltat

t = t + deltat
rate(100)

print(cart.pos)

friction()

==Conceptual Derivation==

It's important to understand why friction exists. Imagine a brick laying at rest on a table as seen below:

==Examples==

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

===Simple===

A 100Kg box is placed on a flat table. The box does not move. The coefficient of static friction <math> {μ}_{s} = {.25} </math> and the coefficient of kinetic friction <math> {μ}_{k} = {.15} </math>.
Find the force of friction <math>{F}_{s}</math>.

Solution:

Since the box does not move, there is only static friction. The normal force is equivalent to the force due to gravity: <math> {F}_{N} = {F}_{g} = {100}{g} </math>. The static friction can be found by: <math> {F}_{s} = {μ}_{s}{F}_{N} </math>

<math> {F}_{s} = {.25}*{100}*{9.8} = {245.25} </math>

===Middling===

A cart of mass 3Kg moves across a track pushed by a fan which exerts <math> {F} = <3,0,1> </math>N with an initial velocity <math> {v}_{i} = <1,0,1>\frac{{m}}{{s}}</math> . Find the required coefficient of kinetic friction <math> {μ}_{k} </math> needed to bring the cart to a stop in 10 seconds.

Solution:

Use the momentum principle: <math>{p}_{f} - {p}_{i} = {F}_{net}{dt}</math> and <math>{F}_{f} = {μ}_{k}{N} </math>

The final velocity must be 0. The initial velocity, initial force, and time are given.

<math>0- <3,0,3> = {F}_{net}*{10s}</math>

<math> {F}_{net} = <-0.3,0,-0.3> </math>

<math> {F}_{net} = {F} - {F}_{f} </math>

<math> <-0.3,0,-0.3> = <3,0,1> - {F}_{f}</math>

<math>{F}_{f} = <3.3,0,1.3> </math>

<math> {F}_{f} = <3.3,0,1.3> = {μ}_{k}{N} </math>

<math> {N} = {3Kg} * {<0,9.8,0>} = <0,29.43,0> </math>

<math> {μ}_{k} = \frac{{F}_{f}}{{N}} = \frac{{<3.3,0,1.3>}}{{0,29.43,0}} </math>

===Difficult===

Two blocks are stacked on top of one another on a frictionless surface. Block A is stacked on top of Block B. Block A has a mass of 2 Kg while Block B has a mass of 4 Kg. The coefficient of friction between the blocks is <math> {μ}_{s} = .35 </math>. Find the maximum amount of force that can be applied to Block A so that the blocks stay together.

Solution:

Momentum Principle:

<math> {p}_{f} - {p}_{i} = {F}_{net}{dt} </math>

We need to find the force of friction at its maximum to find the maximum amount of force that can be exerted on Block A. <math> {F}_{f} = {μ}_{s}{N} </math>

Forces on Block A:

<math> {F}_{A} - {F}_{f} </math>

Forces on Block B:

<math> {F}_{f} </math>

Since we want the blocks to move together, they must therefore have the same acceleration.

<math> {F}_{A} - {F}_{f} = {2 Kg} * {a} </math>

<math> {F}_{f} = {4 Kg} * {a} </math>

<math> {F}_{A} - {F}_{f} = {2 Kg} * {a} </math>

Since they have the same acceleration, we can use the acceleration to solve for the force applied.

<math> {a} = \frac{{F}_{A} - {F}_{f}}{{2 Kg}} </math>

<math> {a} = \frac{{F}_{f}}{{4}} </math>

<math>\frac{{F}_{A} - {F}_{f}}{{2 Kg}}= \frac{{F}_{f}}{{4 Kg}} </math>

<math>{F}_{A}= \frac{{3}}{{2}}{F}_{f} </math>

<math>{F}_{A}= \frac{{3}}{{2}} * {.35}*{6Kg}*{9.8} = {30.87}</math> N

==Connectedness==

Friction is an important topic to understand because it has many industrial implications. Since friction can cause increases in temperature when objects move, engineers who work with moving objects must understand and account for friction to ensure systems work properly. For example, car engines must have proper oil and lubricants to prevent parts from scraping together and wearing down. Mechanical engineers, aerospace engineers, and civil engineers must deal with friction and its impacts every day!

== See also ==

===External links===

Internet resources on this topic

Hyper Physics: http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html#fri

PHET Simulation: https://phet.colorado.edu/en/simulation/friction

==References==
[1] Serway, Raymond A., and John W. Jewett. Physics for Scientists and Engineers. Boston, MA: Cengage Brooks/Cole, 2014. Print.

[2] Sherwood, Bruce A. Matter & Interactions. By Ruth W. Chabay. 4th ed. Vol. 1. N.p.: John Wiley & Sons, 2015. 45-50. Print. Modern Mechanics.

[[Category:Contact Forces]]

2018-11-16T19:45:51Z

IceF1ame:

Alex Reyna claimed 4/18/2018
Blake Castleman claimed 11/16/2018
This page was originally created by ksubramanian33, as can be seen by the edit history.
 

==Main Ideas==
===Conceptual Model===
* The law of conservation of energy states that the total amount of energy of a system before and after an interaction between objects.
* This only applies to isolated systems (no outside forces acting on the system).
** Not Isolated: An object sliding across a rough floor (system = the object). There is work being done by the floor on the object because of the frictional force. Energy lost to heat due to friction is an example of mechanical energy being converted into thermal energy.
** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> [[File:IntroConservationEnergy.gif]] </div> see reference 7
[[File:energy-transformation.jpg]]
see reference 3

===Mathematical Model===
* Single Particle
** Particle Energy: Eparticle = γmc2 
** Rest Energy: Erest = mc2 
** Kinetic (particle): K = γmc2 + mc2 
* General Objects
** Kinetic: (1/2)mv2
** Gravitational Potential: (-Gm1m2)/(R2) (large distances), mgh (near the surface of the Earth)
** Spring (Elastic) Potential: (1/2)kss2 
** Thermal Energy: mCΔT 
====General Formulas====
* E = W + Q (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
* E = K + U (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
These formulas can be interchanged. For example, if you know work and heat transfer are zero, energy equals zero, so K + U will equal zero

[[File:MathConservationEnergy.png]]
 See Reference 2

 [https://www.youtube.com/watch?v=kw_4Loo1HR4 Basic Explanation of Conservation of Energy]
 [https://www.youtube.com/watch?v=EZrJNIBX2wk Skater Visualization of Transfers of Energy]

===Computational Model===
Below is a link to a segment of Vpython code that models the motion of a spring and graphs its kinetic and potential energy. It also shows how the total amount of energy of the system does not change.

"https://trinket.io/embed/glowscript/49c1365501?showInstructions=true"

==Examples==

===Particle===
An electron is accelerated to a speed of 2.95 × 108 
(a) What is the energy of the electron? 
(b) What is the rest energy of the electron? 
(c) What is the kinetic energy of the moving proton? 
(a) 
E = γmc2 
E = (5.50)(9.11 × 10-31)(3 × 108) 
E = 1.50 × 10-21 J 
(b) 
Erest = mc2 
Erest = (9.11 × 10-31)(3 × 108)2 
Erest = 2.73 × 10-22 J 
(c) 
K = E - Erest 
K = 1.50 × 10-21 - 2.73 × 10-22 
K = 1.23 × 10-21 J 

===Simple===
A ball is at rest on a table with 50 J of potential energy. It then rolls of the table, and at one point in time as it falls, the ball has 30 J of kinetic energy. 
What is the potential energy of the ball at that instant?

[[File:EasyEnergyConservation.png]]
 See Reference 3

Einitial = Efinal 
Kinitial + Uinitial = Kfinal + Ufinal 
0 J + 50 J = 30 J + Ufinal 
Ufinal = 20 J

===Middling===
A ball is at rest 50 m above the ground. You then drop the ball. What is its speed before hitting the ground? 
[[File:HardEnergyConservation.gif]]
 See Reference 4 

v = 
√2gh 
 
v = 
√2(9.8)(50) 
 
v = 31.3 m/s

===Difficult===
The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. How fast was the SUV traveling just before the collision? The coefficient of friction between the tires and the road is 0.72.
[[File: DifficultEnergyConservation.png]]
See Reference 5 

KE2 + PE2 = KE3 + PE3 - Wnc 
(1/2)mtotalv22 + mtotalgh2 = (1/2)mtotalv32 + mtotalgh3 - Wnc 
(1/2)mtotalv22 + 0 = 0 + 0 - (μmtotalg)dcos(180°) 
(1/2)v22 = -(0.72)(9.8 m/s2)(8.2 m)(-1) 
v22 = 116 m2/s2 
v2 = 10.8 m/s 

* Notice how the mass is canceled. 

p1 = p2 
p1x = p2x 
msuvvsuv + mcarvcar = mtotalv2 
(1700 kg)vsuv + 0 = (2650 kg)(10.8 m/s) 
(1700 kg)vsuv = 28600 kgm/s 
vsuv = 17 m/s 

==Connectedness==
Industrial Engineering 
1. How is this topic connected to something that you are interested in? 
This concept is clearly connected to physics and helps explain and sometimes predict how objects transform and change as a result of different interactions. Knowing why and how things move and interact is very powerful. 
2. How is it connected to your major? 
This topic is connected to industrial engineering as the field deals heavily with optimization of production processes im manufacturing environments. Obviously, modeling and simulating industrial processes at its core uses the fundamental principles of physics. It is important to take all fundamental concepts of physics, including the conservation of energy, into account. 
3. Is there an interesting industrial application? 
The law of conservation of energy is prevalent in nearly every industrial application of physics. More specifically, it is relevant today as finding renewable and sustainable forms of energy is becoming a more prevalent social and economic issue. It will be interesting to see how this concept will be applied as we try to get more energy for less. Additionally, the law of conservation of energy can be applied at a nuclear microscopic level as radiating particles like alpha particles follow the same energy principle as objects on a macroscopic level. 

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 Who: Many physicists contributed to the knowledge of energy, however it is most notably atributed to Julius Robert Mayer
 What: Most formally discovered the law of conservation of energy
 When: 1842
 Where: Germany
 Why: To explain what happens to energy in an isolated system
 See Reference 6

== See also ==

[[Kinetic Energy]] 
[[Potential Energy]] 
[[Work]] 
===Further reading===

Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction. 
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9. 
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers. 

===External links===
 [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy Khan Academy]
 [http://www.physicsclassroom.com/class/energy/Lesson-2/Application-and-Practice-Questions Practice Questions]
 [http://physics.info/energy-conservation/problems.shtml More Practice]
 [http://gilliesphysics.weebly.com/uploads/5/7/5/2/57520801/conservation_of_energy_practice_problems.pdf Basic Examples] 
[http://www.physnet.org/modules/pdf_modules/m158.pdf The First Law of Thermodynamics]
==References==

1."Conservation of Energy." Hmolpedia. Web. 1 Dec. 2015. <http://www.eoht.info/page/Conservation+of+energy>. 
2. "University of Wisconsin Green Bay." Speed & Stopping Distance of a Roller-Coaster. Web. 1 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/2/>. 
3. "Motion." G9 to Engineering. Web. 1 Dec. 2015. <http://www.g9toengineering.com/resources/translational.htm>. 
4. "Energy of Falling Object." HyperPhysics. Web. 1 Dec. 2015. <http://hyperphysics.phy-astr.gsu.edu/hbase/flobj.html>. 
5. "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>. 
6. "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
7. "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>
8. "Law of Conversation of Energy" ME Mechanical. Web. 18 Apr. 2018. <https://me-mechanicalengineering.com/law-of-conservation-of-energy/>
[[Category:Energy]]