September 14, Tuesday: Lecture 7
--------------------------------

Every Action has an Equal and Opposite Reaction: Newton's Third Law

Examples: When I hit the wall with my fist, the wall hits me back with
          an equal but opposite force. That is why my hand gets hurt.

          We keep the book on a table, the weight of the book (which
          is the force of gravity on the book) is acting on the table.
          But the table is holding the book up (from falling against
          the gravitational force) by applying an equal but opposite
          force upwards against gravity.

          F = mass x acceleration
          W = m x g

          An apple falls on Earth from a tree, because Earth's gravitational
          force (apple's weight=mg) is pulling the apple down. So, the apple
          falls with an acceleration (due to gravity) g (=9.8 m/s2).

          The Apple is also pulling Earth with the same force W. Here,
          the force applied to Earth by the apple = F = M(earth)a(earth).

          But W and F are equal and in opposite direction.
          
          Therefore, m(apple)g(accl of the apple) = Ma 

                a (earth by apple's pull)    m (apple)     
           or, -------------------------- = ---
                g                            M (earth)

since m (apple) << M (earth), i.e., mass of the apple is much smaller than the
mass of Earth, Earth's acceleration due to the apple's pull is also much
smaller than g i.e., a (earth) << g .

Recap Newton's Laws

         First Law: Law of Inertia
         -------------------------

                                    An object at rest or moving at a constant
velocity continues to be in the same state unless a force acts on the object.

         Second Law: F = ma
         -------------------
                                    When a force acts on an object, it produces
an acceleration of the object (proportional to the applied force) in the same 
direction as the applied force. The ratio of the force and the acceleration 
produced by the force is known as the mass of the object.

         Third Law: Action and Reaction
         ------------------------------
                                       Every action has an equal and opposite
reaction.


Aside: Addition and Subtraction of Vectors

       --------> ----->     = --------------> 
         5N        3N              8N

       --------> <-----     = --->
          5N      -3N          2N
                  

       <-------- ----->     = <---   
         -5N       3N           -2N    
              

In general, you can add two vectors by completing a triangle or a xxxxx
where the resultant vector is obtained by the diagonal where the two vectors 
form adjacent sides.


Concept Checks:
---------------

Consider a horse pulling a buggy. Is the following statement true?

The weight of the horse and the normal force exerted by the ground on the horse
constitute an interaction pair that are always equal and opposite according to
Newton's third law.

1. YES
2. NO

Consider a car at rest. We can conclude that the downward gravitational pull
of Earth on the car and the upward contact force of Earth on it are equal and
opposite because 

1. the two forces form an interaction pair.
2. the net force on the car is zero.
3. neither of the above.