Question #d4070

1 Answer
Jan 11, 2017

Answer:

The answer is very simple: the difference is in the object on which the forces act. An action-reaction pair is not canceled. On the other hand, balanced forces do.

Explanation:

Consider the following image:
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Consider case 1:

On a body two forces of the same modulus and direction act but opposite directions, #F_1# and #F_2#. Therefore, the resultant #F_R# of the forces acting on said body is 0, because:

#F_2 = F_1 rArr F_R = F_1 - F_2 = 0#

Instead, let's see what happens in case 2:

Here, we have a body #A# that exerts a force #F_{A//B}# on a body #B#. By virtue of Newton's Third Law, we can state that on the body #A# will appear a force #F_{B//A}# exerted by the body #B#.

That is, to the #F_{A//B}# action responds an #F_{B//A}# reaction.

But these forces, being of equal modulus and opposite senses, do not cancel out. Why? Because they act on different bodies . The resulting force on #A# is #F_R = F_{B//A}#, while on #B# there is a resulting force #F_R = F_{A//B}#. When acting on different bodies they are independent forces and each body will move according to the acceleration that each of these forces provoke on him, i.e.:

#a_A = - {F_{B//A}}/{m_A} color(white) ".................." a_B = {F_{A//B}}/{m_B}#

Where we have assumed that the left-right direction is the positive.