Game Development Reference
In-Depth Information
a rock will have a certain mass, and the mass of the rock is the same whether the rock is on the
surface of the earth or on Jupiter.
Weight, on the other hand, is the force of gravity that acts upon an object. It is equal to the
mass of the object,
m
, times the gravitational acceleration,
g
.
wmg
=
(3.2)
Weight is not an intrinsic property because it depends on gravitational acceleration, which
can vary from place to place. A rock will weigh less on Earth than it will on Jupiter because the
gravitational acceleration on Earth is less than that of Jupiter. A rock that is floating in outer
space is weightless, but it will still have a mass.
For the most part in this topic, we will be working with mass rather than weight. As was
mentioned in Chapter 1, the unit of mass in the SI system is the kilogram or
kg
.
Newton's Third Law of Motion: Equal and Opposite Forces
When people think about forces, it is common to think of one object exerting a force upon
another object. For example, we might think of a baseball bat exerting a force on a baseball
when it strikes the ball. Newton's third law of motion states that there is no such thing as an
isolated force. When a bat exerts a force on the baseball, the baseball exerts an equal and oppo-
site force on the bat. In his
Principia
he wrote
To every action there is always opposed an equal reaction: or the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.
The more commonly used way to express this concept is “for every action there is an equal
and opposite reaction.” There are a lot of everyday examples of Newton's third law in action—
the recoil of a gun, a swimmer pushing off the wall of a pool, and so on. An easy way to test
Newton's third law is to have two people sit in rolling chairs on a hard floor. If one person pushes
on the other chair, both chairs will begin to move in opposite directions. The first person exerted a
force on the second person's chair, but the chair exerted an equal an opposite force on the
person who did the pushing.
Force Vector
Force is a vector quantity in that a force has both a magnitude and a direction. The result of the
force depends on the direction, or
line of action
, of the force. If a gun is shot straight up in the
air, the motion of the bullet due to that force will obviously be different than if the gun is fired
horizontally. When creating physics models that involve forces, it is usually beneficial to split
the overall force vector into directional components. The effect of each directional force can be
evaluated independently of the others, and this approach often simplifies the overall problem.
A force vector is split into directional components according to whatever frame of refer-
ence is being used. If the frame of reference is Cartesian, the force is split into components that
act in the x-, y-, and z-directions.
