Forces that are equal in size and opposite in direction occur for two
completely different reasons: they might be balanced forces on a system that is
not accelerating, or they might be the pair of forces that are related by
the Law of Interaction. To distinguish the two cases, consider the
game being played by Billy, Andrei, Cynthia, Mirella, Carla, and
Frances in this picture.
There is a long catalog of forces acting here:
The force the ground is exerting on Billy
The force that Billy is exerting on the ground
The force that Billy is exerting on the rope
The force that the rope is exerting on Billy
The force that the part of the rope on the left is
exerting on Andrei
The force that Andrei is exerting on the part of the rope to
the left of him
...
and so on, listing the forces involving Cynthia, Mirella, Carla, and Frances, ending with
...
The force that the ground is exerting on Frances.
Balanced Forces
Even though we have all these forces, there is no net force on anyone or anything, because
nothing is moving. The forces are all balancing each other.
For example, the rope is exerting a force on Billy, and the ground is
exerting a sideways force on Billy. These forces are balancing: they are
equal in size and opposite in direction. (The ground is also exerting an
upward force on Billy, which balances the downward force of gravity).
When we discuss balancing forces, we are considering all the forces acting
on a particular object -- such as Billy.
Although the other children are playing a role in the game, we don't need
to consider them individually if they are not directly exerting a force on Billy --
for instance, by pulling on his shirt.
In the example pictured, the other children are only connected to Billy by way of the rope.
When accounting for balancing forces, we only need to show the forces acting directly
on Billy, such as the force of the rope.
So far as Billy is concerned, it doesn't matter how hard each person was pulling.
Balanced forces, again
In the tug of war, the rope is also not moving. This means that the forces on it must balance.
There are lots of them:
The force that Billy is exerting on the rope (to the left)
The force that Andrea is exerting on the rope (to the right)
The force that Cynthia is exerting on the rope (to the right)
The force that Mirella is exerting on the rope (to the right)
The force that Carla is exerting on the rope (to the right)
The force that Frances is exerting on the rope (to the right)
What "balancing" means in this example is that the sum of the forces to the right is equal to the
sum of the forces to the left. Billy is exerting a large force on his end of the rope, and
Andrei, Cynthia, Mirelle, Carla, and Frances are exerting smaller forces that add up to the same large
force, in the opposite direction.
Law of Interaction Forces
The condition that forces are in balance relates a certain set of forces. The
Law of Interaction gives a different set of relationships.
In the picture above, we identified the force that the rope exerts on Billy.
But according to the Law of Interaction, there must be another force in the
situation: the force Billy exerts on the rope.
These two forces involve the same two things: Billy and the rope. If you give
the full name of the forces, it is easy to tell that these are the ones that
are related by the Law of Interaction:
The force the rope exerts on Billy.
The force Billy exerts on the rope
The condition that forces are in balance relates a certain set of forces. The
Law of Interaction gives a different set of relationships.
In the picture above, we identified the force that the rope exerts on Billy.
But according to the Law of Interaction, there must be another force in the
situation: the force Billy exerts on the rope.
These two forces involve the same two things: Billy and the rope. If you give
the full name of the forces, it is easy to tell that these are the ones that
are related by the Law of Interaction: