Transcript Chapter 6 Force and Motion II

Chapter 6 Force and Motion II
6.2. Friction
6.3. Properties of Friction
6.4. The Drag Force and Terminal Speed
6.5. Uniform Circular Motion
The Friction Force
There are two types of friction forces:
• Kinetic Friction Forces
• Static Friction Forces
Kinetic Friction Forces
An object is experiencing a kinetic friction force
when the object is moving relative to a surface.
• Kinetic friction forces is linearly proportional to the
normal force.
• The slope of Kinetic friction forces vs. the normal force is
changing for different surfaces.
Kinetic Friction Forces
The magnitude of the kinetic friction force
can be expressed as:
The slope μkin is called the coefficient of kinetic
friction and N is the magnitude of the normal force.
Question
A person has a choice of either pushing
or pulling a sled at a constant velocity, as
the drawing illustrates. Friction is
present. If the angle θ is the same in
both cases, does it require less force to
push or to pull? Account for your answer.
Example 1 Sled Riding
A sled is traveling at 4.00 m/s along a
horizontal stretch of snow, as Figure
illustrates. The coefficient of kinetic friction
is μk=0.0500. How far does the sled go
before stopping?
Static Friction Forces
An object is experiencing a static friction
force when the object intend to move (but
not move yet) relative to the surface.
Properties of Static Friction Forces
• The magnitude fs of the static frictional force can have any
value from zero up to a maximum value of depending on
the applied force.
• The maximum static friction is:
f sMax   s N
The μs is the coefficient of static friction, and N is the
magnitude of the normal force.
•The coefficient of static friction is usually larger than the
coefficient of kinetic friction
Example 2 The Force Needed to Start a Sled
Moving
A sled is resting on a horizontal patch of
snow, and the coefficient of static friction is
μs=0.350. The sled and its rider have a
total mass of 38.0 kg. What is the
magnitude of the maximum horizontal
force that can be applied to the sled before
it just begins to move?
Example 3
A House on a Hill A house is built on the top of a hill with
a nearby 45° slope (Fig. 6-42). An engineering study
indicates that the slope angle should be reduced
because the top layers of soil along the slope might slip
past the lower layers. If the static coefficient of friction
between two such layers is 0.5, what is the least angle φ
through which the present slope should be reduced to
prevent slippage?
Example 4
Block on a Slab A 40 kg slab rests on a
frictionless floor. A 10 kg block rests on top of
the slab (Fig. 6-58). The coefficient of static
friction between the block and the slab is 0.60,
whereas their kinetic friction coefficient is 0.40.
The 10 kg block is pulled by a horizontal force
with a magnitude of 100 N. What are the
resulting accelerations of (a) the block and (b)
the slab?
Example 5
Body A in Fig. weighs 102 N, and body B weighs 32 N.
The coefficients of friction between A and the incline are
and . Angle is 40°. Let the positive direction of an x
axis be up the incline. In unit-vector notation, what is the
acceleration of A if A is initially (a) at rest, (b) moving up
the incline, and (c) moving down the incline?
Drag Force
The magnitude of the drag
force is related to the
relative speed:
1
D  C  Av 2
2
• C is drag coefficient
• ρ is the air density (mass per
volume)
• A is the effective crosssectional area of the body (the
area of a cross section taken
perpendicular to the velocity ).
Terminal Speed
When sky diving, a terminal speed will be
reached when drag force is equal to the
gravity.
Centripetal Force
A centripetal force accelerates a body by changing
the direction of the body’s velocity without changing
the body’s speed.
Important: a centripetal force is not a special type of force.
Sample Problem
6
In a 1901 circus
performance, Allo “Dare
Devil” Diavolo introduced
the stunt of riding a
bicycle in a loop-the-loop
(Fig. 6-10a). Assuming
that the loop is a circle
with radius , what is the
least speed v Diavolo
could have at the top of
the loop to remain in
contact with it there?
Sample Problem 7
Curved portions of highways are always
banked (tilted) to prevent cars from
sliding off the highway. When a highway
is dry, the frictional force between the
tires and the road surface may be
enough to prevent sliding. When the
highway is wet, however, the frictional
force may be negligible, and banking is
then essential. Figure 6-13a represents
a car of mass m as it moves at a
constant speed v of 20 m/s around a
banked circular track of radius R=190m .
(It is a normal car, rather than a race car,
which means any vertical force from the
passing air is negligible.) If the frictional
force from the track is negligible, what
bank angle θ prevents sliding?
Conceptual Questions
•
Suppose that the coefficients of static and kinetic friction
have values such that μs=2.0μk for a crate in contact with
a cement floor. Does this mean that the magnitude of the
static frictional force acting on the crate at rest would
always be twice the magnitude of the kinetic frictional
force acting on the moving crate? Give your reasoning.
• A box rests on the floor of an elevator. Because of static
friction, a force is required to start the box sliding across
the floor when the elevator is (a) stationary, (b)
accelerating upward, and (c) accelerating downward.
Rank the forces required in these three situations in
ascending order—that is, smallest first. Explain.
• During the final stages of descent, a sky
diver with an open parachute approaches
the ground with a constant velocity. The
wind does not blow him from side to side.
Is the sky diver in equilibrium and, if so,
what forces are responsible for the
equilibrium?