134
Self-Checks
1. When a baseball player slides in to a base, is the friction static, or kinetic.
2. A mattress stays on the roof of a slowly accelerating car. Is the friction static
or kinetic.
3. Does static friction create heat. Kinetic friction.
The maximum possible force of static friction depends on what kinds of
surfaces they are, and also on how hard they are being pressed together. The
approximate mathematical relationships can be expressed as follows:
F
s
= –F
applied
, when |F
applied
| <
µ
s
|F
N
| ,
where
µ
s
is a unitless number, called the coefficient of static friction, which
depends on what kinds of surfaces they are. The maximum force that static
friction can supply,
µ
s
|F
N
|, represents the boundary between static and
kinetic friction. It depends on the normal force, which is numerically equal
to whatever force is pressing the two surfaces together. In terms of our
model, if the two surfaces are being pressed together more firmly, a greater
sideways force will be required in order to make the irregularities in the
surfaces ride up and over each other.
Note that just because we use an adjective such as “applied” to refer to a
force, that doesn’t mean that there is some special type of force called the
“applied force.” The applied force could be any type of force, or it could be
the sum of more than one force trying to make an object move.
The force of kinetic friction on each of the two objects is in the direc-
tion that resists the slippage of the surfaces. Its magnitude is usually well
approximated as
|F
k
|=
µ
k
|F
N
|
where
µ
k
is the coefficient of kinetic friction. Kinetic friction is usually more
or less independent of velocity.
(1) It’s kinetic friction, because her uniform is sliding over the dirt. (2) It’s static friction, because even though the
two surfaces are moving relative to the landscape, they’re not slipping over each other. (3) Only kinetic friction
creates heat, as when you rub your hands together. If you move your hands up and down together without sliding
them across each other, no heat is produced by the static friction.
We choose a coordinate system in
which the applied force, i.e. the force
trying to move the objects, is positive.
The friction force is then negative,
since it is in the opposite direction. As
you increase the applied force, the
force of static friction increases to
match it and cancel it out, until the
maximum force of static friction is sur-
passed. The surfaces then begin slip-
ping past each other, and the friction
force becomes smaller in absolute
value.
applied
force
friction
force
static frictionkinetic friction
Chapter 5Analysis of Forces