Nuzhat: /* Newton's Third Law of Motion */

2012-09-10T18:32:49Z

Newton's Third Law of Motion

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===Newton's Three Laws of Motion===


====Newton's First Law of Motion====

''"A body continues in a state of rest, or of uniform motion in a straight line, unless acted upon by an external force."''
 
In other words, an object remains at rest or moves at constant velocity when

<math>\Sigma \vec{F} = 0</math> 

Newton’s first law is based on the principle of inertia. The tendency of a body to resist a change in its state of motion is called '''inertia'''. 

*[[Inertia|MORE ON INERTIA]]

 
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====Newton's Second Law of Motion====

''"An object of mass <math>m</math> moves with an acceleration that is defined by <math>\Sigma \vec{F} = ma</math>."''
 
Thus, the acceleration of a body is directly proportional to the net force acting on the body, and is inversely proportional to its mass.

 
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====Newton's Third Law of Motion====

''"For every action there is an equal and opposite reaction."''
 
<math>\vec{F_{12}} = -\vec{F_{21}}</math>

In other words, if body <math>1</math> applies a force on body <math>2</math>, then body <math>2</math> applies an equal and opposite force on body <math>1</math>.
 
Convention for the subscripts: If a force is exerted by an object A on an object B then we write this force as follows:

<math>\vec{F_{AB}}</math>

 
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*Focus on notation: The first subscript <math>A</math> indicates the particle which exerts the force; the second subscript <math>B</math> indicates the particle on which the force is exerted. For example, the normal force exerted by the floor (<math>F</math>) on a box (<math>B</math>) in the diagram below should be labelled

<center><math>\vec{F_{FB}}</math> </center>

[[image:Newtons_Third_Law_Notation.png|TOP]] 

*Action/reaction pairs: The two forces <math>F_1</math> and <math>F_2</math> form an action-reaction pair if and only if the two forces are of the same type (a normal force and a gravitational force cannot be an action-reaction pair) and if and only if we can write that

<center><math>F_1</math> is exerted by an object B on an object A and</center>

<center><math>F_2</math> is exerted by an object A on an object B.</center>

For example: <math>{F_G}_{EM}</math> which is a gravitational force exerted by the Earth on the man and <math>{F_G}_{ME}</math> which is a gravitational force exerted by the man on the Earth are the action-reaction pair.

On the other hand, <math>{F_G}_{EM}</math> which is a gravitational force exerted by the Earth on the man and <math>{F_N}_{SM}</math> which is the normal force exerted by the surface of the Earth on the man are not the action-reaction pair. 

*Application of these concepts to find the acceleration of systems — problem solving strategy:

#Define a system of particles that you will study — each particle should be dealt with separately;
#List external forces acting on each particle use the notation which indicates the agent and then draw arrows to represent each external force in the diagram;
#Draw a free body diagram for each particle:
#*Select and draw an "appropriate" coordinate system for each particle so that
#**The x-axis is parallel to the direction in which a particle may possibly move or the direction of possible acceleration;
#**The orientation of the x-axis for each particle in the system must be in the same sense;
#**The positive y-axis is oriented +90º from the positive x-axis.
#*Transfer the arrows representing forces into this system (each arrow has the tail at the origin).
#*Determine the angle <math>\theta</math> each arrow makes with the positive x-axis.
#Write all forces in terms of their x- and y-components: for a given force of magnitude <math>F</math> and direction <math>\theta</math>, <math>F_x = F \cos\theta</math> and <math>F_y = F \sin \theta</math>
#Write equations for each particle <math>\Sigma F_x = 0</math> or <math>\Sigma F_x = ma</math>
#Write equations for each particle <math>\Sigma F_y = 0</math>
#Identify all the action-reaction pairs.
#Solve the system of equations. 

*An overview of the forces acting on a body in a mechanical system:

#Gravitational force: <math>F_G = {G m_1 m_2 \over r^2}</math>
#Special case of a gravitational force (close to the surface of Earth): <math>F_G = mg</math>
#Contact forces: Tension, Normal force and Friction.
#Force of a spring: restoring force <math>F = -kx</math>
#Tension is caused by a restoring force acting between particles of thin long objects: rope, rod, beam, string, etc.
#The direction of the tension is always parallel to the thin object.
#Normal force is caused by a restoring force acting between particles of surfaces; it is always perpendicular to the surface.
#Friction occurs when two surfaces are in contact. It is due to an interaction between surface particles of one object and surface particles of the second object.



===Exercises===

*[[Applications Of Newton's First and Second Laws]] 

*[[Applications Of Newton's Third Law]]

Newton's Laws - Revision history

Nuzhat: /* Newton's Third Law of Motion */