Download Lecture 8.MoreForces..

More Forces
Lecturer:
Professor Stephen T. Thornton
Reading Quiz: You try to move a heavy
couch around your living room. When
does the maximum friction occur?
A) When you push so hard that it almost
moves, but it does not move, because it is
so heavy.
B) When you move it slowly on the floor.
C) When two people move it at a faster speed
on the floor.
D) Right when it almost stops moving.
Answer: A
Static friction is generally larger than kinetic
friction.
Last Time
Forces
Free body diagrams
Weight and mass
Normal force
Tension
Lots of conceptual quizzes
Work Problems
Today
Review
Friction
Accelerated Mass. A particle of
mass m, initially at rest at x  0, is
accelerated by a force that increases
2
in time as F  Ct . Determine its
velocity and position x as a function
of time.
Conceptual Quiz: A person hoists a bucket from a well
using a rope. Let the bucket be at rest. She then ties
the other end of the rope to the handle. In which case
is the tension in the rope the greatest?
A
A. Case A
B. Case B
C. They are the same
B
Answer: A
Common Forces Revisited
Tension
Tension always pulls, never pushes.
For light (negligible-mass) ropes, the magnitude of the
tension is the same everywhere along the rope.
The Normal Force
Normal force is always perpendicular to surface.
It is self adjusting unless structure is too weak.
Applying Newton’s Laws with Constant Forces
If force is constant, acceleration is constant:
These equations apply to each component:
x, y, z.
Conceptual Quiz
A block of mass m rests on the
floor of an elevator that is
moving upward at constant
speed. What is the relationship
between the force due to gravity
and the normal force on the
block?
A) N > mg
B) N = mg
C) N < mg (but not zero)
D) N = 0
E) depends on the size of the
elevator
v
m
Conceptual Quiz
A block of mass m rests on the
floor of an elevator that is moving
upward at constant speed. What is
the relationship between the force
due to gravity and the normal force
on the block?
A) N > mg
B) N = mg
C) N < mg (but not zero)
D) N = 0
E) depends on the size of the
elevator
The block is moving at constant
speed, so it must have no net force
on it. The forces on it are N (up)
and mg (down), so N = mg, just like
the block at rest on a table.
v
m
Friction is always present when two
solid surfaces slide along each other.
The microscopic details
are not yet fully
understood.
Copyright © 2009 Pearson Education, Inc.
Facts about friction
• Leonardo da Vinci performed
experiments on friction
(~1500). He found it was the
normal force that was
important, not the surface area.
• Show block on table.
• Friction is bad. $1B of
research/year.
• Friction is good. Many
examples; we walk, drive cars,
etc.
Kinetic Friction and the Normal Force
Constant velocity.
F   fk
2 F  2 f k
Do demo
Experimental results
It requires a certain force to overcome
friction. Energy is used up.
Experiments (done in 1429) show
f k  k N (not a vector result)
The subscript k indicates kinetic (or
sliding) friction. We use the terms
kinetic and sliding interchangeably.
Experimental Results
You will do these experiments in lab.
Sliding friction is also called kinetic friction.
Approximation of the frictional force fk :
f k = mk FN
Here, FN (or N) is the normal force, and μk is
the coefficient of kinetic friction, which is
different for each pair of surfaces.
Copyright © 2009 Pearson Education, Inc.
More experimental results
 Friction is proportional to the
magnitude of the normal force.
 Friction is independent of the
relative speed of the surfaces.
 Friction is (to first order)
independent of the area of contact
between surfaces.
We are examining kinetic friction.
Static friction
In kinetic or sliding friction the two objects
are moving with respect to each other.
In static friction the object is at rest, but we
want it to move. We have to overcome
friction to have it move. We find there is a
certain amount of force needed to do this.
Example of static friction
Do demo
Experimental result for static friction
There is an upper limit of static
friction that we have to overcome in
order to move an object.
Static friction can have any value up
to this maximum amount.
0  fs  fs,max
fs, max  s N
These are concepts!
Facts about static friction
Static friction can have any value from
zero to its maximum amount.
Value:
0  fs  fs,max
Static friction is independent of area of
contact between surfaces.
Static friction is parallel to surface of
contact, and in the direction that
opposes the relative motion.
When we walk,
is it static friction
or kinetic friction
when our feet are
in contact with
the ground?
Answer: static
Same with car
tires.
Do coefficient of friction
measurement.
fS
N
N = W cos q
f S £ mS N = mSW cos q
W cos q q
f S = W sin q
also
W
q
W sin q
f S = mSW cos q = W sin q
mS = tan q
when block moves
Note that, in general, μs > μk.
Conceptual Quiz
An object is held in place by friction on an
inclined surface. The angle of inclination
is slowly increased until the object starts
to move. If the surface is kept at this
angle when it first moves, the object
A)
B)
C)
D)
speeds up.
moves at uniform speed.
slows down.
soon stops.
Answer: A
We just did this experiment.
Remember that the coefficient of
static friction is greater than that of
kinetic friction. So when static
friction is overcome and the object
starts sliding, the kinetic frictional
force becomes smaller, and the net
force (due to gravity) is down the
plane.
Conceptual Quiz:
A block of mass m is pulled in the direction
shown in the figure across a rough surface at
constant velocity. The magnitude of the frictional
force is
A. k m g
B.
C.
D.
E.
k T cosq
k (T - mg)
k T sinq
T cosq
Answer: E
Because the velocity is constant,
there is no horizontal net force.
Therefore the horizontal component
of the tension (Tcosq) must have the
same magnitude as the frictional
force, which is the only other
horizontal force. This also has the
magnitude
k (mg  T sinq )
Forces when pushing box from dead start:
Pushing Box on Vertical Wall. A small
box is held in place against a rough
vertical wall by someone pushing on it
with a force directed upward at 28° above
the horizontal. The coefficients of static
and kinetic friction between the box and
wall are 0.40 and 0.30, respectively. The
box slides down unless the applied force
has magnitude 23 N. What is the mass of
the box?