Game Development Reference
In-Depth Information
There are a couple of interesting things to note about spring forces. First of all, a spring
exerts a restoring force, one that acts to restore the spring to its equilibrium position. If the
spring at its equilibrium position is pulled to the right to a new length
l
, as shown in Figure 3-7,
the spring force on the object doing the pulling will be directed to the left. The restoring nature
of the force is the reason for the negative sign in Equation (3.10).
l
F = k(l-l
o
) F = -k(l-l
o
)
Figure 3-7.
A spring exerts an equal and opposite restoring force when deflected.
Another interesting thing about springs is that they exert a variable force in that the spring
force increases with increasing deflection of the spring from its equilibrium position. As the
spring moves back towards its equilibrium position, the force exerted on either end of the spring
steadily decreases.
The final topic we will discuss about springs is the damping force associated with them.
According to Hooke's Law, if a spring with a weight on the end of it is extended and released, it
will oscillate forever about its equilibrium location. Of course, in reality this perpetual motion
doesn't occur and the spring motion gradually decreases until the spring comes to a rest. The
gradual decrease in motion is due to a damping force that is proportional to the difference in
velocity of the two ends of the spring.
(
)
Fkvv
=−
(3.11)
d
d
2
1
The damping force,
F
d
, serves to reduce the acceleration of the spring. We'll revisit
Hooke's Law and damping forces in Chapter 4 when we discuss spring motion.
Exercise
3.
A spring with a spring constant of 325
N/m
hangs vertically from a ceiling. If a 1
kg
mass is attached to the end
of the spring, how much lower will the end of the spring be when it reaches its new equilibrium position?
Centripetal Force
Force, acceleration, and velocity are vectors and have a direction as well as a magnitude. We
have also learned that a force is required for a change in velocity to occur. These two facts lead
to an interesting situation that occurs when an object is traveling at a constant velocity
v
around
a circle with a radius
r
as shown in Figure 3-8.
