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

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