Graphics Reference
In-Depth Information
produced. The impulse force is a short-duration force that is applied normal to the surface of contact on
each of the two objects. Calculation of the impulse force due to collision is discussed in
Chapter 7
,
Section 4.2
. Other important examples of contact forces are friction and viscosity.
Friction
Friction arises from the interaction of surfaces in contact. It can be thought of as resulting from the
multitude of collisions of molecules caused by the unevenness of the surfaces at the microscopic level.
The frictional force works against the relative motion of the two objects. Frictional forces from a
surface do not exceed an amount proportional to the normal force exerted by the surface on the object.
This is stated in
Equation B.114
,
where
s
is the coefficient of static friction and
f
N
is the normal force
(component of the force that is perpendicular to the surface). Variable
s
varies according to the two
materials that are in contact.
f
s
¼ sf
N
(B.114)
The frictional forces acting between surfaces at rest with respect to each other are called
forces of
static friction
. For a force applied to an object sitting on another object that is parallel to the surfaces in
contact, there will be a specific force at which the block starts to slip. As the force increases from zero
up to that threshold force, the lateral force is counteracted by an equal force of friction in the opposite
direction. Once the object begins to move,
kinetic friction
acts on the object and approximately obeys
the empirical law of
Equation B.115
,
where
k
is the coefficient of kinetic friction and
f
N
is the force
normal to the surface. Kinetic friction is typically less than static friction. The force of kinetic friction is
always opposite to the velocity of the object.
f
k
¼ kf
N
(B.115)
Viscosity
The resistive force of an object moving in a medium is
viscosity
. It is another contact force and is
extremely difficult to model accurately. When an object moves at low velocity through a fluid, the
viscosity is approximately proportional to the velocity (
Eq. B.116
)
;
K
is the constant of proportionality,
which depends on the size and the shape of the object, and
n
is the coefficient of viscosity, which
depends on the properties of the fluid. The coefficient of viscosity,
n
, decreases with increasing tem-
perature for liquids and increases with temperature for gases. Stokes's law for a sphere of radius
R
is
given in
Equation B.117
.
F
vis
¼Knv
(B.116)
K ¼
6
pR
(B.117)
An object dropping through a liquid attains a constant speed, called the limiting or terminal veloc-
ity, at which gravity, acting downward, and the viscous force, acting upward, balance each other and
there is no acceleration (e.g.,
Eq. B.118
for a sphere). Terminal velocity is given by
Equation B.119
.In
a viscous medium, heavier bodies fall faster than lighter bodies. For spherical objects falling at a low
velocity in a viscous medium, not necessarily at terminal velocity, change in momentum is given by
mg ¼
6
pRnv
(B.118)
Search WWH ::
Custom Search