Game Development Reference
In-Depth Information
and pulls the block across the plane. The perpendicular component produces the
force holding the block to the plane:
Nmg θ
=
cos
.
(13.103)
The force
F due to kinetic friction is given by
F μ N μ mg θ
=−
=−
cos
(13.104)
K
K
K
and acts in the direction opposite that of F . The acceleration a of the block is
equal to the net force acting on it divided by its mass:
F
+
F
G
K
a
=
=
g θμg θ
sin
cos
.
(13.105)
K
Plugging in the angle of inclination and coefficient of kinetic friction, we obtain
the result
1
3
(
)
(
)
2
2
2
a
=
9.8 m s
0.5
9.8 m s
0.656 m s
.
(13.106)
2
2
Notice that the mass of the block is inconsequential.
The static friction force prevents an object on a surface from moving by op-
posing any tangential force that may be acting on it. The maximum force
F that
can be exerted due to static friction is given by
F μ N
=−
,
(13.107)
S
S
where N is the normal force and μ is called the coefficient of static friction .
Again, we use a minus sign to indicate that the force acts in the direction opposite
that of any force trying to move the object. Typical values of
μ for various sur-
faces are listed in Table 13.1.
As soon as a force on an object exceeds the maximum value of F given by
Equation (13.107), the object begins to move, and the static friction force is re-
placed by the kinetic friction force
, so less
force is required to move an object once it has been set in motion than was re-
quired to initiate the motion.
F . It is often the case that
F
<
F
K
S