Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 561

box forward on the ground. The box weighs twice as much as Moe, and
he has placed it on a cart that rolls with very little friction. According to
Newton's third law, the box pushes back on Moe. But then why does the
box accelerate and Moe doesn't? It doesn't look like there are “equal and
opposite actions” happening here.
Conundrums such as these are always resolved by considering all the
forces acting on both bodies. In the example just discussed, Moe is not
floating in midair, or else he would have been accelerated backwards just
as Newton's third law predicts he would. (Consider what would happen
if Moe and the box were on ice.) No, Moe is standing on the ground.
Through the force of friction, Moe pushes against the Earth and the Earth
pushes back on Moe. In fact, if we assume that Moe makes some forward
progress instead of just being stuck there grunting, then the force of the
Earth pushing against him must exceed the force of the box pushing back
against him, and he accelerates forward. This is illustrated in Figure 12.3.
Figure 12.3
The four forces
involved in Moe
pushing the box
An inquisitive reader might wonder about the previous scenario, “Why
doesn't the Earth then accelerate?” The short answer is, “It does!” A
medium-length answer is, “It does, in the short run.” For the full length
answer, we have to wait until Section 12.3, which tells us a little bit about
momentum.
Of course, these theoretical questions are certainly interesting to pon-
der, but what practical application is there for Newton's third law? The
most important application, for our purposes, is the justification to sim-
plify a rigid body and treat it as a single particle. For example, earlier we
considered the forces acting on a large beam in a skyscraper. What if the