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Newton's Laws of Motion
Law 1  
A body will continue in a state of rest or uniform motion unless acted on by an external force.  
Often called the law of inertia:  
The inertia of a body is a measure of its reluctance to change the state of its motion.  
This gives us the concept of "inertial mass".  
(Bodies having large mass are reluctant to change... try standing in front of a moving truck !)  
   
Law 2  
The net (or resultant) force acting on a body is equal to the product of its mass and its acceleration.  
Net (resultant) force = mass acceleration  
∑ F = ma  
click here for experimental verification of this law    
   
Law 3  
If body A exerts a force on body B then body B exerts an equal magnitude but opposite sense force on body A.  
   
This statement reminds us that the term "a force" should always be considered as describing an interaction between two bodies and that both the bodies experience the same magnitude of interaction.  
   
This, of course, does not mean that the effect of the interaction will be the same on the two bodies: think again about the "standing in front of a moving truck" example above.  
   
In Law 2 above, the symbol ∑F means the sum of forces.  
 
If the forces act along the same line, as above, the arithmetic is trivial:  
If F1 has magnitude 4N and F2 has magnitude 10N then the magnitude of ∑F (the resultant force) is simply given by +10 + (-4) = 6N  
 
Remember that force is a vector quantity.  
This reminds us that this sum will often be a vector sum.  
We use bold letters to represent vectors.  
 
If the two forces shown above act on a body then ∑F means that we must do a vector addition to find the resultant of the two forces.  
   
If the magnitude of F1 is 3N and the magnitude of F2 is 4N, then the magnitude of their resultant FR is 5N acting at about  48.6 to F2  
click here for a reminder about vector addition  
   
Example: Using Newton's Second Law of Motion  
An object of mass m = 20kg rests on a horizontal surface.  
Calculate the magnitude of the force exerted by the surface on the object in the following situations.  
   
a) Surface stationary or moving with constant velocity  
Since the forces all act in the same line in this example, ∑F will represent the simple arithmetic sum.  
∑F = ma          Newton's law  
also  
∑F = R + mg          sum of (magnitudes of) forces  
but, here a = 0   
R + mg = 0   
R = -mg = 196  
(remember g is directed in the negative sense, as defined here)  
   
b) Surface accelerating upwards at 2ms-2  
   
∑F = ma          Newton's law  
also  
∑F = R + mg          sum of (magnitudes of) forces  
but, here a = +2ms-2  
R + mg = ma    so    R = m(a - g)   
therefore  
R = 20(2 - (-9.8)) = 236N  
   
   
   
c) Surface accelerating downwards at 9.8ms-2  
∑F = ma          Newton's law  
   
∑F = R + mg          sum of (magnitudes of) forces  
but, here a = -9.8ms-2  
R + mg = ma    so    R = m(a - g)   
therefore  
R = 20(-9.8 - (-9.8)) = 0N    
and, in this case, the body is said to be "weightless"  
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