What is the amount of tension in
the rope?
ȈF = ma
T + (ímg) = ma
T = 19 N (upward)
5.13 - Newton's second and third laws
It might seem that Newton’s third law could lead to the conclusion that forces do not
cause acceleration, because for every force there is an equal but opposite force. If for
every force there is an equal but opposite force, how can there be a net non-zero force?
The answer lies in the fact that the forces do not act on the same object. The pair of
forces in an action-reaction pair acts on different objects. In this section, we illustrate
this often confusing concept with an example.
Consider the box attached to the rope in Concept 1. We show two pairs of action-
reaction forces. Normally, we draw all forces in the same color, but in this illustration,
we draw each pair in a different color. One pair is caused by the force of gravity. The
force of the Earth pulls the box down. In turn, the box exerts an upward gravitational
force of equal strength on the Earth.
There is also a pair of forces associated with the rope. The tension of the rope pulls up
on the box. In response, the box pulls down on the rope. These forces are equal but
opposite and form a second action-reaction pair. (Here we only focus on pairs that
include forces acting on the box or caused by the box. We ignore other action-reaction
pairs present in this example, such as the hand pulling on the rope, and the rope pulling
on the hand.)
Now consider only the forces acting on the box. This means we no longer consider the forces the box exerts on the Earth and on the rope. The
two forces on the box are gravity pulling it down and tension pulling it up. In this example, we have chosen to make the force of tension greater
than the weight of the box.
The Concept 2 illustration reflects this scenario: The tension vector is longer than the weight vector, and the resulting net force is a vector
upward. Because there is a net upward force on the box, it accelerates in that direction.
Now we will clear up another possible misconception: that the weight of an object resting on a surface and the resulting normal force are an
action-reaction pair. They are not. Since they are often equal but opposite, they are easily confused with an action-reaction pair. Consider a
block resting on a table. The action-reaction pair is the Earth pulling the block down and the block pulling the Earth up. It is not the weight of the
block and the normal force.
Here is one way to confirm this: Imagine the block is attached to a rope pulling it up so that it just touches the table. The normal force is now
near zero, yet the block’s weight is unchanged. If the weight and the normal force are supposed to be equal but opposite, how could the normal
force all but disappear? The answer is that the action-reaction pair in question is what is stated above: the equal and opposite forces of gravity
between the Earth and the block.
Action-reaction pairs
Two pairs involving box:
·Gravity
·Tension & response