Game Development Reference
R ESTING F ORCES
When an object is resting on another, Newton's third and final law of motion comes
into play. Newton 3 states: “For every action there is an equal and opposite reaction.”
We already used this law in chapter 14 for collisions involving two objects. When we
calculated the impulse on one object, we applied the same impulse in the opposite
direction to the second object. Collisions between objects and the immovable envi-
ronment used the assumption that any movement of the environment would be so
small that it could be safely ignored. In reality, when an object bounces on the ground,
the whole earth is also bouncing: the same impulse is being applied to the earth. Of
course the earth is so heavy that if we tried to work out the amount of motion that
the earth undergoes, it would be vanishingly small, so we ignore it.
When we come to resting contacts, a similar process happens. If an object is rest-
ing on the ground, then the force of gravity is trying to pull it through the ground.
We feel this force as weight: the force that gravity is applying on a heavy object is
great. What isn't as obvious is that there is an equal and opposite force keeping the
object on the ground. This is called the “reaction force,” and Newton 3 tells us that it
is exactly the same as its weight. If this reaction force were not there, then the object
would accelerate down through the ground. Figure 15.1 shows the reaction force.
Whenever two objects are in resting contact and not accelerating, there will be
a balance of forces at the point of contact. Any force that one object applies to the
other will be met with an equal reaction force back. If this balance of forces isn't
present, then both objects will be accelerating. We can work out the acceleration using
Newton's second law of motion, after working out the total force (including reaction
forces) on each object.
There is something of a circular process here, and it gives a taste of some issues to
come. If reaction forces can be as large as necessary (we're assuming rigid bodies will
never crumble or compress), and acceleration depends on the total forces applied,
how do we calculate how big the reaction forces actually are at any time? For simple
situations like that in figure 15.1, this isn't a problem, and in most high school and
F IGURE 15.1
A reaction force at a resting contact.