Compression or Normal Force: Difference between revisions

Latest revision as of 16:14, 17 June 2019

The Main Idea

The compression force, most commonly known as the normal force, [math]\displaystyle{ F_N }[/math], is a simple fundamental concept that must be understood before attempting any contact-force problems. First, it is important to understand that the normal force is NOT a kind of fundamental force, such as the electric or gravitational force. It is a force used to describe the interactions between atoms in contact. As hinted by the name, this force simply points in the perpendicular/normal/orthogonal direction to the surface(s) that the object is in contact with. The magnitude of the normal force is often equal to the weight of the object ([math]\displaystyle{ F_g }[/math]), however, objects can move along surfaces with various angles. This results in the normal force being present at an angle to the horizontal. Understanding information about the normal force on an object can also help to finding the magnitude of other forces present in a system, such as the force of friction.

A Mathematical Model

Since the normal force is completely dependent upon on how much force the object is exerting on the surface, there is no single equation to describe it. However, there a 3 main cases that will likely come up:

1) An object lays on a flat surface with no forces pushing up or down on the object, besides gravity:

The normal force ([math]\displaystyle{ F_N }[/math]) will be equal in magnitude and opposite in direction of the weight or gravitational force ([math]\displaystyle{ F_g }[/math]) on the object:

[math]\displaystyle{ F_N = F_g = Mg }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object and [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity.

2) An object lies on an angled surface with no forces pushing up or down on it, besides gravity:

The normal force [math]\displaystyle{ F_N }[/math] will be equal to the magnitude of the vertical component of the gravitational force ([math]\displaystyle{ F_{g_y} }[/math]) on the object:

[math]\displaystyle{ F_N = F_g \ \text{cos}(\theta) = Mg \times \text{cos}(\theta) }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object, [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity, and [math]\displaystyle{ \theta }[/math] is the angle between the horizontal and the angled surface.

3) An object lies on a surface, which may be angled (a) or not (b), with a force pushing down on the object:

a) An object lays on an angled surface with a force, such as an applied force, pushing down on the object. The normal force [math]\displaystyle{ F_N }[/math] will be equal to the vertical component of the gravitational force on the object plus the component of the extra force that pushes straight down (if the extra force is angled, so that it is not perfectly vertical, only the vertical component will increase the normal force):

[math]\displaystyle{ F_N = F_g \ \text{cos}(\theta) + F = Mg \times \text{cos}(\theta) + F }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object, [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity, [math]\displaystyle{ \theta }[/math] is the angle between the horizontal and the angled surface, and [math]\displaystyle{ F }[/math] is the extra force pushing down on the object.

---or---

[math]\displaystyle{ F_N = F_g \ \text{cos}(\theta) + F \ \text{sin}(\phi) = Mg \times \text{cos}(\theta) + F \times \text{sin}(\phi) }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object, [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity, [math]\displaystyle{ \theta }[/math] is the angle between the horizontal and the angled surface, [math]\displaystyle{ F }[/math] is the extra force pushing down on the object, and [math]\displaystyle{ \phi }[/math] is the angle between the horizontal and the extra force [math]\displaystyle{ F }[/math].

b) An object lays on a flat surface with a force, such as an applied force, pushing down on the object. The normal force [math]\displaystyle{ F_N }[/math] will be equal to the magnitude of the gravitational force on the object plus the component of the extra force that pushes straight down (if the extra force is angled, so that it is not perfectly vertical, only the vertical component will increase the normal force):

[math]\displaystyle{ F_N = F_g + F = Mg + F }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object, [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity, and [math]\displaystyle{ F }[/math] is the extra force pushing down on the object.

---or---

[math]\displaystyle{ F_N = F_g + F \ \text{sin}(\phi) = Mg + F \times \text{sin}(\phi) }[/math]

[math]\displaystyle{ M }[/math] is the mass of the object, [math]\displaystyle{ g }[/math] is the acceleration on the object due to gravity, [math]\displaystyle{ F }[/math] is the extra force pushing down on the object, and [math]\displaystyle{ \phi }[/math] is the angle between the horizontal and the extra force [math]\displaystyle{ F }[/math].

It is useful to note the frictional force ([math]\displaystyle{ F_f }[/math]) is defined in terms of the normal force ([math]\displaystyle{ F_N }[/math]) by:

[math]\displaystyle{ F_f = \mu F_N }[/math]

[math]\displaystyle{ \mu }[/math] is the characteristic coefficient of friction between the two materials in contact.

A Computational Model

from __future__ import division

from visual import *

from visual.graph import *

scene.title = "Normal Force"

scene.background = color.black

scene.center = (0.7, 1, 0)

inclinedplane = box(pos = vector(0.6, 0, 0), size = (1.2, 0.02, 0.2), color = color.green, opacity = 0.5)

cart = box(size = (0.2, 0.06, 0.06), color = color.red)

trail = curve(color = color.yellow, radius = 0.01)

cart.m = 0.5

cart.pos = vector(0, 0.04, 0.08)

cart.v = vector(0,0,0)

theta = 25 * (pi / 180.0)

cart.v = norm(inclinedplane.axis)

cart.v.mag = 3

inclinedplane.rotate(angle = theta, origin = (0,0,0), axis = (0,0,1))

cart.rotate(angle = theta, origin = (0,0,0), axis = (0,0,1))

g = 9.8

M = cart.m

F = 100

t = 0

dt = 0.005

while cart.pos.y > 0.02:

   rate(1000)
   F_N = M * g * cos(theta)
   a = norm(inclinedplane.axis)
   a.mag = g * sin(theta)
   cart.v = cart.v + a*dt
   cart.pos = cart.pos + cart.v*dt
   trail.append(pos = cart.pos)

   t = t+dt
   print("Normal Force:", F_N)

Examples

The simplest normal force problem involves an object resting on a flat surface with only gravity and the normal force acting on the object. To raise the difficulty a little, one may position the object on an inclined plane, so that the normal force is now at an angle. Finally, other considerations such as incorporating a tension force or applied force could demonstrate other difficulties.

Simple

A [math]\displaystyle{ 7 \ \text{kg} }[/math] block rests on a flat table.

a) Find the normal force ([math]\displaystyle{ F_N }[/math]) that is being exerted on the block:

Since the block is at rest on a flat surface, we know the net force ([math]\displaystyle{ F_{net} }[/math]) must be [math]\displaystyle{ 0 }[/math]:

[math]\displaystyle{ F_{net} = \sum F = Ma = 0 }[/math]

We also know that only the normal force ([math]\displaystyle{ F_N }[/math]) and the gravitational force are acting on the block ([math]\displaystyle{ F_g }[/math]). Therefore, they must be equal in magnitude and opposite in direction. Since we know gravity is acting straight downwards, the normal force must act straight upwards.

Summing these forces gives:

[math]\displaystyle{ F_{net} = F_g - F_N = 0 }[/math]

Therefore:

[math]\displaystyle{ F_N = F_g = Mg = 7 \times 9.81 = 68.67 \ \text{Newtons} }[/math]

Middling

A [math]\displaystyle{ 14 \ \text{kg} }[/math] block is lying on an inclined plane that makes an angle [math]\displaystyle{ \theta \ \text{of} \ 48^\text{o} }[/math] with the horizontal.

a) Find the normal force ([math]\displaystyle{ F_N }[/math]) acting on the block:

First, we know the normal force ([math]\displaystyle{ F_N }[/math]) will be perpendicular to the inclined plane. Hence, it will be convenient to use a coordinate plane where the x-axis is parallel to the inclined plane, and the y-axis is perpendicular to the inclined plane. With this coordinate system, the normal force should be along the y-axis, which is convenient.

Second, the only force acting along the y-axis other than the normal force is the gravitational force ([math]\displaystyle{ F_g }[/math]). Therefore, if we can find the y-component of the gravitational force, we will be able to find the normal force.

Finally, since the block is at rest with respect to the y-axis, we know its acceleration along the y-axis ([math]\displaystyle{ a_y }[/math])must be [math]\displaystyle{ 0 }[/math].

We start with Newton's Second Law along the y-axis:

[math]\displaystyle{ F_{net} = \sum F_y = F_{g_y} - F_N = F_g \text{cos}(\theta) - F_N = Ma_y = 0 }[/math]

Therefore:

[math]\displaystyle{ F_N = F_g \times \text{cos}(\theta) = Mg \times \text{cos}(48^\text{o}) = 91.90 \ \text{Newtons} }[/math]

Difficult

In a pulley system, a block of mass [math]\displaystyle{ M }[/math] is hanging over the edge of an inclined plane that makes an angle [math]\displaystyle{ \alpha }[/math] with the horizontal. It is attached to another block of mass [math]\displaystyle{ m }[/math]. The block of mass [math]\displaystyle{ m }[/math] is sliding upwards on the ramp as the block of mass [math]\displaystyle{ M }[/math] is slowly moving downwards.

a) Draw a free body diagram for the block of mass [math]\displaystyle{ M }[/math] and the block of mass [math]\displaystyle{ m }[/math]:

b) Find the normal force ([math]\displaystyle{ F_N }[/math]) acting on the block of mass [math]\displaystyle{ m }[/math]:

We know the normal force ([math]\displaystyle{ F_N }[/math]) must be normal to the inclined plane. We can see from our free body diagram for the block of mass [math]\displaystyle{ m }[/math], the only forces working perpendicular to the inclined plane are a component of gravity and the normal force. Using this realization, Newton's Second Law, and the fact that [math]\displaystyle{ a_{\perp} }[/math] must equal [math]\displaystyle{ 0 }[/math], we can sum the forces perpendicular to the surface to find the normal force acting on the block of mass [math]\displaystyle{ m }[/math]:

[math]\displaystyle{ F_{\perp} = F_{g_{\perp}} - F_N = ma_{\perp} = 0 }[/math]

Therefore:

[math]\displaystyle{ F_N = F_{g_{\perp}} = mg \times \text{cos}(\alpha) }[/math]

Connectedness

The normal force is very crucial to our understanding of everyday life because of its endless necessity, application, and usefulness. It is the reason why gravity doesn't keep pulling us down and explains this not-so-apparent force that is acting on an object. Why can you place your textbooks on your desk and not have to worry about them falling through? The normal force. The application of the normal force can be seen in many industrial situations, where the weights of large objects must be watched. Also, it must be taken into account when drawing free body diagrams, such as for construction and architectural purposes.

History

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Sir Isaac Newton

The normal force is a direct application of Newton's Third Law of Motion. Sir Isaac Newton was a famous scientist from England who roamed the Earth from 1643 to 1727. His work in math and physics set the stage for many of the principles and theories that we have today. His main work, the Philosophiae Naturalis Principia Mathematic, discussed many of his theories about physics and stated his three laws of motion. The application of Newton's Third Law of Motion extends strongly into the modern era due to the high prevalence of the normal force in real world situations, such as landing a rocket on the moon.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html

Images:

https://en.wikipedia.org/wiki/Normal_force#/media/File:Friction_relative_to_normal_force_(diagram).png

https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica

https://en.wikipedia.org/wiki/Friction

http://www.texample.net/tikz/examples/free-body-diagrams/

Compression or Normal Force: Difference between revisions

Latest revision as of 16:14, 17 June 2019

Contents

The Main Idea

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See also

Further Reading

External links

References

Navigation menu

@@ Line 1: / Line 1: @@
-Claimed by Hemanth Koralla
-[[File:Normal force.png|right|thumb|''F<sub>N</sub>'' represents the '''normal force''']]
+==The Main Idea==
+[[File:Normal force.png|right|300px|thumb|''F<sub>N</sub>'' represents the '''normal force''']]
-==Compression of Normal Force==
+The compression force, most commonly known as the normal force, <math>F_N</math>, is a simple fundamental concept that must be understood before attempting any contact-force problems. First, it is important to understand that the normal force is '''NOT''' a kind of fundamental force, such as the electric or gravitational force. It is a force used to describe the interactions between atoms in contact. As hinted by the name, this force simply points in the perpendicular/normal/orthogonal direction to the surface(s) that the object is in contact with. The magnitude of the normal force is often equal to the weight of the object (<math>F_g</math>), however, objects can move along surfaces with various angles. This results in the normal force being present at an angle to the horizontal. Understanding information about the normal force on an object can also help to finding the magnitude of other forces present in a system, such as the force of friction.
-The compression or also commonly known as the normal force, <math>F_n</math>, is a simple fundamental concept that must be understood before attempting any contact force problem. First, it is important to understand that the normal force is NOT a kind of fundamental force such as the electric or gravitational force. It is just a force used to describe the interaction between atoms. As hinted by the name, this force simply points in the perpendicular or "normal" direction to the surface(s) that it is in contact with. The magnitude of this normal force is often equal to the weight of the object, however, objects can move along surfaces with various angles. This results in the normal force being present in both the direction parallel and perpendicular to the surface. Understanding information about the normal force on an object can also help to finding the magnitude of other forces present in a system, such as the force of friction.
-==== Equations ====
+===A Mathematical Model===
-The formula for calculating the normal force is dependent on the positioning of the system, however, the most commonly used formula for normal force is represented below:
-:<math>F_n = mg </math>
-:<math>F_n </math> is the normal force of the system
-:<math>m</math> is the mass of the system
-:<math>g</math> is a constant value for the  force due to gravity and is equivalent to 9.8 <math>m/s^2</math>
+Since the normal force is completely dependent upon on how much force the object is exerting on the surface, there is no single equation to describe it. However, there a 3 main cases that will likely come up:
-The formula for calculating the force of friction using this normal force when an object situated on an angle is:
+:'''1) An object lays on a flat surface with no forces pushing up or down on the object, besides gravity:'''
-:<math>F_f (static) = (\mu)F_n </math>
-:<math>= (\mu)mg \cos(\theta))</math>
+::The normal force (<math>F_N</math>) will be equal in magnitude and opposite in direction of the weight or gravitational force (<math>F_g</math>) on the object:
-:<math> (\mu) </math> = coefficient of static or kinetic friction
-:<math>m</math> is the mass of the system
+:::<math>F_N = F_g = Mg</math>
-:<math>g</math> is a constant value for the  force due to gravity and is equivalent to 9.8 <math>m/s^2</math>
+::::<math>M</math> is the mass of the object and <math>g</math> is the acceleration on the object due to gravity.
+:'''2) An object lies on an angled surface with no forces pushing up or down on it, besides gravity:'''
+::The normal force <math>F_N</math> will be equal to the magnitude of the vertical component of the gravitational force (<math>F_{g_y}</math>) on the object:
+:::<math>F_N = F_g \ \text{cos}(\theta) = Mg \times \text{cos}(\theta)</math>
+::::<math>M</math> is the mass of the object, <math>g</math> is the acceleration on the object due to gravity, and <math>\theta</math> is the angle between the horizontal and the angled surface.
+:'''3) An object lies on a surface, which may be angled ('''a''') or not ('''b'''), with a force pushing down on the object:'''
+::'''a) An object lays on an angled surface with a force, such as an applied force, pushing down on the object. The normal force <math>F_N</math> will be equal to the vertical component of the gravitational force on the object plus the component of the extra force that pushes straight down (if the extra force is angled, so that it is not perfectly vertical, only the vertical component will increase the normal force):
+::::<math>F_N = F_g \ \text{cos}(\theta) + F = Mg \times \text{cos}(\theta) + F</math>
+:::::<math>M</math> is the mass of the object, <math>g</math> is the acceleration on the object due to gravity, <math>\theta</math> is the angle between the horizontal and the angled surface, and <math>F</math> is the extra force pushing down on the object.
+:::<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><big>'''---or---'''</big></div>
+::::<math>F_N = F_g \ \text{cos}(\theta) + F \ \text{sin}(\phi) = Mg \times \text{cos}(\theta) + F \times \text{sin}(\phi)</math>
+:::::<math>M</math> is the mass of the object, <math>g</math> is the acceleration on the object due to gravity, <math>\theta</math> is the angle between the horizontal and the angled surface, <math>F</math> is the extra force pushing down on the object, and <math>\phi</math> is the angle between the horizontal and the extra force <math>F</math>.
+::'''b) An object lays on a flat surface with a force, such as an applied force, pushing down on the object. The normal force <math>F_N</math> will be equal to the magnitude of the gravitational force on the object plus the component of the extra force that pushes straight down (if the extra force is angled, so that it is not perfectly vertical, only the vertical component will increase the normal force):
+::::<math>F_N = F_g + F = Mg + F</math>
+:::::<math>M</math> is the mass of the object, <math>g</math> is the acceleration on the object due to gravity, and <math>F</math> is the extra force pushing down on the object.
+:::<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><big>'''---or---'''</big></div>
+::::<math>F_N = F_g + F \ \text{sin}(\phi) = Mg + F \times \text{sin}(\phi)</math>
+:::::<math>M</math> is the mass of the object, <math>g</math> is the acceleration on the object due to gravity, <math>F</math> is the extra force pushing down on the object, and <math>\phi</math> is the angle between the horizontal and the extra force <math>F</math>.
+It is useful to note the frictional force (<math>F_f</math>) is defined in terms of the normal force (<math>F_N</math>) by:
+:<math>F_f = \mu F_N</math>
+::<math>\mu</math> is the characteristic coefficient of friction between the two materials in contact.
+===A Computational Model===
+<code>
+from __future__ import division
+from visual import *
+from visual.graph import *
+scene.title = "Normal Force"
+scene.background = color.black
+scene.center = (0.7, 1, 0)
+inclinedplane = box(pos = vector(0.6, 0, 0), size = (1.2, 0.02, 0.2), color = color.green, opacity = 0.5)
+cart = box(size = (0.2, 0.06, 0.06), color = color.red)
+trail = curve(color = color.yellow, radius = 0.01)
+cart.m = 0.5
+cart.pos = vector(0, 0.04, 0.08)
+cart.v = vector(0,0,0)
+theta = 25 * (pi / 180.0)
+cart.v = norm(inclinedplane.axis)
+cart.v.mag = 3
+inclinedplane.rotate(angle = theta, origin = (0,0,0), axis = (0,0,1))
+cart.rotate(angle = theta, origin = (0,0,0), axis = (0,0,1))
+g = 9.8
+M = cart.m
+F = 100
+t = 0
+dt = 0.005
+while cart.pos.y > 0.02:
+    rate(1000)
+    F_N = M * g * cos(theta)
+    a = norm(inclinedplane.axis)
+    a.mag = g * sin(theta)
+    cart.v = cart.v + a*dt
+    cart.pos = cart.pos + cart.v*dt
+    trail.append(pos = cart.pos)
+    t = t+dt
+    print("Normal Force:", F_N)
+</code>
 ==Examples==
+The simplest normal force problem involves an object resting on a flat surface with only gravity and the normal force acting on the object. To raise the difficulty a little, one may position the object on an inclined plane, so that the normal force is now at an angle. Finally, other considerations such as incorporating a tension force or applied force could demonstrate other difficulties.
-The examples below represent different situations in which the net force changes due to the placement of the system.
+===Simple===
+[[File: ExampleNorm1.png|right|300px|thumb|Example 1]]
-===Simple===
+A <math>7 \ \text{kg}</math> block rests on a flat table.
+:'''a) Find the normal force (<math>F_N</math>) that is being exerted on the block''':
-[[File: ExampleNorm1.png|left|thumb|Example 1]]
+::Since the block is at rest on a flat surface, we know the net force (<math>F_{net}</math>) must be <math>0</math>:
-On the image to the left (Example 1),a7 kilogram block rests on top a flat table. Find the normal force, <math> F_n\ </math>, that is being exerted on the block.
+:::<math>F_{net} = \sum F = Ma = 0</math>
-The force of gravity is <math>9.8 m/s^2</math>.
+::We also know that only the normal force (<math>F_N</math>) and the gravitational force are acting on the block (<math>F_g</math>). Therefore, they must be equal in magnitude and opposite in direction. Since we know gravity is acting straight downwards, the normal force must act straight upwards.
-====Answer====
+::Summing these forces gives:
-Using the provided free body diagram, the net force acting on the block is equal to the normal force minus the gravitational force. Since the object is at rest, the net force is equal to zero. This allows the normal force to be set equal to the gravitational force generate the formula <math>F_n = mg</math>. Plugging in the given values into the equation will yield the correct results.
-Given:
-<math>m = 7kg </math>
-<math>g = 9.8 m/s^2</math>
-<math> F_n = mg</math>
-<math>F_n = (7 kg)(9.8 m/s^2)</math>
-<math> = 68.6 N</math>
+:::<math>F_{net} = F_g - F_N = 0</math>
+::Therefore:
+:::<math>F_N = F_g = Mg = 7 \times 9.81 = 68.67 \ \text{Newtons}</math>
 ===Middling===
 [[File: InclinedPlane.jpg|200px|right|Example 2]]
-A 14 kg block is lying stationary on a plane that is inclined 48 degrees. Find the normal force perpendicular to the block on the incline using the accompanying image to the right.
+A <math>14 \ \text{kg}</math> block is lying on an inclined plane that makes an angle <math>\theta \ \text{of} \ 48^\text{o}</math> with the horizontal.
-The force of gravity is <math>9.8 m/S^2</math>.
+:'''a) Find the normal force (<math>F_N</math>) acting on the block''':
+::First, we know the normal force (<math>F_N</math>) will be perpendicular to the inclined plane. Hence, it will be convenient to use a coordinate plane where the x-axis is parallel to the inclined plane, and the y-axis is perpendicular to the inclined plane. With this coordinate system, the normal force should be along the y-axis, which is convenient.
+::Second, the only force acting along the y-axis other than the normal force is the gravitational force (<math>F_g</math>). Therefore, if we can find the y-component of the gravitational force, we will be able to find the normal force.
-====Answer====
+::Finally, since the block is at rest with respect to the y-axis, we know its acceleration along the y-axis (<math>a_y</math>)must be <math>0</math>.
-Because this problem asks for the normal force on an inclined plane, it is important to break up the normal force into components:
-Given:
+::We start with Newton's Second Law along the y-axis:
-<math>m = 14 kg</math>
-<math>g = 9.8 m</math>
-<math>(\theta) = 48</math>
-By analyzing the image, it is seen that the cosine trig identity correlates to the direction in which the normal force is perpendicular to the surface. Multiplying the mass of the block and force of gravity by the cosine of the stated angle, the perpendicular normal force will be found.
+:::<math>F_{net} = \sum F_y = F_{g_y} - F_N = F_g \text{cos}(\theta) - F_N = Ma_y = 0</math>
-<math>F_n = mgcos(\theta)</math>
+::Therefore:
-<math>F_n = (14 kg)(9.8 m/s^2)cos(48)</math>
-<math> = 91.805 N</math>
+:::<math>F_N = F_g \times \text{cos}(\theta) = Mg \times \text{cos}(48^\text{o}) = 91.90 \ \text{Newtons}</math>
 ===Difficult===
-In a pulley system, block 1 of mass <math>M_1</math> is hanging over the edge of an inclined plane at an angle, <math>(\alpha)</math> where it is attached to block 2 of mass <math>M_2</math>. Block 2 is sliding upwards on the ramp as block 1 is slowly moving downwards. Draw a free body diagram for block 1 and block 2 and find the parallel component of the net force, <math>F_n</math> for block 2.
+In a pulley system, a block of mass <math>M</math> is hanging over the edge of an inclined plane that makes an angle <math>\alpha</math> with the horizontal. It is attached to another block of mass <math>m</math>. The block of mass <math>m</math> is sliding upwards on the ramp as the block of mass <math>M</math> is slowly moving downwards.
+:'''a) Draw a free body diagram for the block of mass''' <math>M</math> '''and the block of mass''' <math>m</math>:
+[[File:Free-body-diagrams.jpg|center|Example 3]]
+:'''b) Find the normal force''' (<math>F_N</math>) '''acting on the block of mass''' <math>m</math>:
-====Answer====
+::We know the normal force (<math>F_N</math>) must be normal to the inclined plane. We can see from our free body diagram for the block of mass <math>m</math>, the only forces working perpendicular to the inclined plane are a component of gravity and the normal force. Using this realization, Newton's Second Law, and the fact that <math>a_{\perp}</math> must equal <math>0</math>, we can sum the forces perpendicular to the surface to find the normal force acting on the block of mass <math>m</math>:
-The free body is as shown below:
-[[File:Free-body-diagrams.jpg|center|Example 3]]
+:::<math>F_{\perp} = F_{g_{\perp}} - F_N = ma_{\perp} = 0</math>
+::Therefore:
-Since the question is asking for the parallel component of the net force, it would be helpful to draw a triangle that depicts the trigonometric quantities <math>sin(\alpha)</math> and <math> cos(\alpha)</math> (see Example 2 image for reference). The component that is parallel to the surface on which block 2 is moving on is <math>M_2gsin(\alpha)</math>. This shows that the parallel component of the net force is, <math> F_n = M_2gsin(\alpha)</math>.
+:::<math>F_N = F_{g_{\perp}} = mg \times \text{cos}(\alpha) </math>
 ==Connectedness==
-This force is very crucial to understand because it explains the fundamental reason for why gravity doesn't keep pulling us down and explains this not-so-apparent force that is acting on an object. It helps explain why objects do not keep falling into the Earth. The application of the normal force can be seen in many industrial situations. It must be taken into account when drawing free body diagrams, such as for construction and architectural purposes.
+The normal force is very crucial to our understanding of everyday life because of its endless necessity, application, and usefulness. It is the reason why gravity doesn't keep pulling us down and explains this not-so-apparent force that is acting on an object. Why can you place your textbooks on your desk and not have to worry about them falling through? The normal force. The application of the normal force can be seen in many industrial situations, where the weights of large objects must be watched. Also, it must be taken into account when drawing free body diagrams, such as for construction and architectural purposes.
 ==History==
@@ Line 90: / Line 194: @@
 [[File:SirNewton16.jpg|right|thumb|Sir Isaac Newton]]
-The normal force a direct application of Newton's Third Law of Motion. Sir Isaac Newton was a famous scientist from England who roamed the Earth from 1643 to 1727. His work in math and physics set the stage for many of the principles and theories that we have today. His main work, the Philosophiae Naturalis Principia Mathematic, discussed many of his theories about physics and stated his three laws of motion. The application of Newton's thrid laws of motion extends to today's uses due to the high prevalence of the normal force in real world situations, such as landing a rocket on the moon.
+The normal force is a direct application of Newton's Third Law of Motion. Sir Isaac Newton was a famous scientist from England who roamed the Earth from 1643 to 1727. His work in math and physics set the stage for many of the principles and theories that we have today. His main work, the ''Philosophiae Naturalis Principia Mathematic'', discussed many of his theories about physics and stated his three laws of motion. The application of Newton's Third Law of Motion extends strongly into the modern era due to the high prevalence of the normal force in real world situations, such as landing a rocket on the moon.
 == See also ==
+===Further Reading===
+:[[Inclined Plane]]<br>
+:[[Free Body Diagram]]<br>
+:[[Tension]]<br>
 ===External links===
-http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
+:http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
-http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces
+:http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces
-https://www.physics.uoguelph.ca/tutorials/fbd/FBD3.htm
+:https://www.physics.uoguelph.ca/tutorials/fbd/FBD3.htm
 ==References==
-Information:
+'''Information''':
-https://en.wikipedia.org/wiki/Normal_force
+:https://en.wikipedia.org/wiki/Normal_force
-http://www.sparknotes.com/physics/dynamics/newtonapplications/section1.rhtml
+:http://www.sparknotes.com/physics/dynamics/newtonapplications/section1.rhtml
-http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
+:http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
-Images:
+'''Images''':
-https://en.wikipedia.org/wiki/Normal_force#/media/File:Friction_relative_to_normal_force_(diagram).png
+:https://en.wikipedia.org/wiki/Normal_force#/media/File:Friction_relative_to_normal_force_(diagram).png
-https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica
+:https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica
-https://en.wikipedia.org/wiki/Friction
+:https://en.wikipedia.org/wiki/Friction
-http://www.texample.net/tikz/examples/free-body-diagrams/
+:http://www.texample.net/tikz/examples/free-body-diagrams/
-[[Category: Contact Interactions]]
+:[[Category: Contact Interactions]]