Game Development Reference
In-Depth Information
Exercise
2.
An aluminum box with a mass of 2
kg
is placed on a steel plate that is initially placed on a flat, level surface. One
edge of the plate is lifted such that the plate is now at an inclined angle. If the edge of the plate is continually
lifted thereby increasing the inclined angle, at what angle will the aluminum box begin to slide down the plate?
Springs
Gravity and friction are forces that you will deal with all the time in your game programming
physics models. Less commonly used, but still important in some circumstances, is the force
generated by springs. Typically, we think of a spring as a metal or plastic coil, but objects with
other shapes can exhibit spring-like behavior. In an archery simulation, the bow acts like a
spring. A diving board acts like a spring; so does a catapult.
■
Tidbit
Metal springs have been around since the Bronze age. The development of precision springs
occurred in the Renaissance period and was driven by a need to build precision timepieces for celestial
navigation.
A typical coiled spring that is attached to a wall and resting on the ground is shown in
Figure 3-6. When no force is applied to either end of the spring, it has an equilibrium length
l
0
.
If the spring is deflected from its equilibrium position to a new location
l
, a force is exerted by
the spring on whatever is connected at the two ends. If the spring is attached to a wall and you
pull on it with your finger, the spring will exert an equal and opposite force on both your finger
and the wall. A relation known as
Hooke's Law
describes the force,
F
S
, exerted at either end of
the spring.
l
o
Figure 3-6.
A typical spring
(
)
S
Fk l
=−
−
l
(3.10)
0
The spring constant,
k
, in Equation (3.10) is a material and structural property of the spring
that characterizes the stiffness of the spring. A stiffer spring will have a larger spring constant.
Hooke's Law can also be used to determine the force necessary to achieve a specified deflection
for a given spring. For example, to deflect a spring with a spring constant value of 400
N/m
a
distance of 0.01
m
from its equilibrium position would require a force of 4
N
.
