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 La gare de Montparnasse
train wreck - Paris 1895 |
The second law, Fnet = ma, represents an invitation to analyze a situation in which forces are acting on some object. By deducing the vector sum of all of these forces, one can determine the the acceleration that an object of a given mass will have. The trick here is to find all of the forces because sometimes they are not quite so obvious. Let's take a few lines to take inventory of the forces we are likely to encounter. Along the way it will be prudent for us to consider which forces act parallel to the motion of the object and which lie in the direction perpendicular to motion; the former case cause the object to move faster or slower, the latter change its direction |
a. APPLIED FORCES - these are the pushes and pulls supplied by people, ropes, and other agents. These forces are necessary when change is desired, say when we wish an object to speed up or slow down or change direction. They are not in evidence when an object is moving with uniform speed in a straight line
b. WEIGHT - weight is a manifestation of the gravitational force that the Earth has on an object. Why an object weighs what it does will be considered later when we consider the law of universal gravitation. Most often, the weight of an object is given by the product of the mass of the object times the local acceleration due to gravity. We usually write this as FG = mg or w = mg. The value of g varies ever-so-slightly from site to site on the Earth depending on altitude. Unless otherwise indicated, we will take g to equal 9.80 m/s/s. The force of gravity always points down toward the center of the Earth.
c. NORMAL FORCE - This force is often overlooked by novice physicists. If a block is resting on a table surface, the force due to gravity is acting downward on the object. The table must be supplying an upward force on the block; otherwise, the block would fall to the floor. The normal force is the upward reaction force to the gravitational force that causes the block to press against the table. If the table can muster the reaction force, the block is supported; if not, the block comes crashing down. The normal force always points away from the surface and is always perpendicular to the surface. A very mundane application of normal force that becomes a very dramatic event is a collapsed bridge. The next time you cross a bridge, ask yourself, "is this bridge strong enough to support me and this car". Check out these web sites.
A bathroom scale does not measure
the weight of an object. Rather, it measures normal force. Under
conditions of use for which it was intended, say a person standing
on the scale (no tricks), the downward force of gravity is exactly
balanced by the upward normal force from the scale. Hence the
reading on the scale tells the normal force and therefore the
weight. But what happens if a person stands on the scale and we
choose to push down on her shoulders. The downward forces acting
on our subject are her weight and the external force we apply.
The bathroom scale will supply an equal and opposite upward force
on our subject that can be read on the scale. This force is the
normal force and is greater than her weight.
D. Inclined Plane
When a block rests on a frictionless
plane, say a table, the downward force of gravity is counterbalanced
by the upward force (Normal Force) provided by the table. Even
with no friction , we do not expect the block to move. If we lift
one end of the table, the horizontal plane becomes inclined and
we get a situation where the two forces are not colinear anymore.
The normal force still points away from the surface and is still
perpendicular to it. The force of gravity still points down. We
can resolve the force of gravity into two parts--mgsin(theta)
and mgcos(theta).
mgsin(theta) is the component of gravity that causes things
to slide or roll down hills. When theta is zero, sin theta is
zero; nothing moves. When theta us 90o, the sin of 90 is 1 and
the force acting on the block is MG, the force of gravity. At
some angle in between, sin theta is between zero and one, the
force causing the block to slide down the hill is greater than
zero but less than MG.
mgcos(theta) is the component of MG that is equal to the normal
force. This component becomes important when dealing with friction.
see this useful applet
http://www.lon-capa.org/~mmp/applist/si/plane.htm
E. Weightlessness
This type of reasoning leads us to the
notion of weightlessness. Given that we defined weight = mg some
paragraphs above, w = 0 might imply that m= 0 or that g = 0. An
object with no mass is a silly notion (save for neutrinos and
the like). And Newton's law of universal gravitation will imply
that g is never really equal to zero. Weightlessness occurs in
that circumstance when an object is placed on a bathroom scale
and the scale reads zero. Most commonly, the object and the scale
are in free fall. Gravity is pulling downward, the scale is unable
to supply a reaction force and it therefore reads zero.
AT the moment of first consciousness, and every moment thereafter,
we are caught in a squeeze play that has gravity pulling down
on us and a normal force pushing up. Only for very short periods
are we excused from the squeeze: when seated in a chair if one
leans on the back legs of the chair and leans too far, the rush
one feels is weightlessness. The thrill of skydiving involves
risking a sure death for an extended period of weightlessness.
We cannot shield a space from gravity (as we can for electric-
and magnetic fields). So how is ir that we can witness test subjects
floating in a room in mid-air? The room is actually the cargo
area of a C-147 cargo plane that is flown to a high altitude and
allowed to free-fall. During this time our test subjects can do
everything that skydivers can do; afterall, why should their behavior
be any different just because they are enclosed in a large box
that is also falling with them. The advantage that our friends
have over skydivers is that they can rrelive the experience without
the need to deploy a parachute, land and take off again. The weightless
scenes in movies such as Apollo
13 were shot on a set built into
such a plane.
F. - FRICTION - Friction
is a force that tends to oppose motion
and usually arises as a reaction force a la Newton's third law.
Frictional forces do not exist on an object unless the object
is moving or some force is trying to move it. Friction is an example
of anon-conservative
force, that is,
a force that dissipates energy as it is applied,
most often turning that energy into heat. Friction can be beneficial
if you are trying to walk across an icy walkway. At the same time
friction is no friend if you are trying to drag a heavy crate
across the floor.
As it happens, the frictional force an object encounters as it
interacts with its surroundings depends on how (or if ) it is
moving. First , there is static friction which
occurs when two surfaces are at rest with respect to each other.
The amount of friction depends on the smoothness (or lack thereof)
of the two surfaces. If the two surfaces are moving with respect
to each other, we encounter kinetic friction (a.k.a.
sliding) friction. Kinetic friction is somewhat less than static
friction which has some bearing on the inadvisability of locking
automobile brakes in a panic stop. Then there is fluid
friction, wherein the object in question moves through air, water,
or some other non-solid. A variation on this theme occurs when
a fluid is used as a lubricant because fluid friction can be less
than static or kinetic friction. We will deal with air resistance
only in qualitative terms in this course because the amount of
fluid friction encountered by an object move through air is not
constant. Instead, air resistance varies with the square of the
speed of the object. A quantitative treatment of this topic will
involve calculus. Let it be sufficient to say that an automobile
encounters some air resistance at 25 miles/hour, four times that
air resistance at 50 miles hour, and nine times that resistance
at 75 miles/hour.
\See this applet first before continuing
http://jersey.uoregon.edu/vlab/KineticEnergy/index.html
Try this applet
http://www.lon-capa.org/~mmp/kap8/beam/beam.htm
here is an interesting applet
summarizing many aspects of his topic
http://www.lon-capa.org/~mmp/kap4/cd095a.htm
Related to this applet is Atwood's machine
http://www.lon-capa.org/~mmp/kap4/cd097a.htm
http://www.msu.edu/user/brechtjo/physics/atwood/atwood.html
Let us consider the simple case of a
block being dragged across a table top. We find empirically that
the ratio of the frictional
force to the normal force is constant.
That constant is called the coefficient of friction and is given
the symbol u. FF / FN = u or
more commonly FF = u FN. The coefficient of friction is so-called because
it has no units. Typically, the value of u is between zero and
one, although it could be larger. Reducing the frictional force
between two surfaces is fundamentally a task of reducing the value
of u. In those cases seen earlier in the kinematics section, we
set u = 0 when we neglected friction. We can also regulate the
amount of friction extant between two surfaces by altering the
normal force between them. While dragging a block across the table,
we encounter more friction if we press down on the block, thereby
increasing the upward normal force supplied by the table. We could
also increase the normal force by using a C-clamp to fasten the
block to the table.
An important consideration in dealing with friction and the equation
FF
= u FN is
that the equation will tell you how
much friction is available rather than
how much is actually acting on the object. Consider a block that
weighs 10 N resting on a horizontal table. The normal for is 10
N upward. If u = .3, then the frictional force available is 3
N. A force of 2 N is applied to the block causes the frictional
force of 2 N to oppose the motion and the block does not move.
(If all 3 N of frictional force had been applied, there would
have been a net force in the direction of the frictional force.
It would thus be possible to use friction to move things in some
direction by simply tugging on the object in the opposite direction.)
INCLINED PLANES Our common experience tells us that if we place an object at the top of a hill it may slide down if the hill is steep enough or, at least, if we minimize friction. To the question "why does the object move down the hill?" comes the answer "gravity". But it is also our common experience that an object moving down a hill does not experience the same acceleration as an object in free fall. We find that by some analysis of the forces involved that it is not the full amount of gravitational force (FG = mg) that moves the object but instead a component of this force mgsinq , where q is the angle of inclination above the horizontal . Because sin q increases with increasing angle, sin q = 1 when q = 90 degrees. Thus. we see that steepness of the hill does make a difference, even if the mathematics of the situation is a bit more complicated than we might wish to accept.
Sample
problem - inclined plane,
no friction
Sample
problem - inclined plane, with friction
See these inclined plane applets
http://www.ngsir.netfirms.com/englishhtm/Incline.htm
http://zebu.uoregon.edu/1998/ph101/ex4.html
http://muse.tau.ac.il/~museum/java/pc/LawOfFall/english/act_inclined_eng.html
http://jersey.uoregon.edu/vlab/FMA/
http://zebu.uoregon.edu/nsf/friction.html
http://www.mta.ca/faculty/science/physics/ntnujava/forceDiagram/forceDiagram.html
http://chris.kingsu.ab.ca/~brian/alberta_learning/applets/applet_incline/incline_friction.html
A hallmark of mechanics is the consideration of word problems.
Useful relationships are published here in a page called EQUATIONS. The reader should consult
this page before attempting the problems assigned.
see also
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Go to problems at U. Oregon http://zebu.uoregon.edu/~dmason/probs/mech/newt.html |
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Supplementary Problems 2 |
This page was last reviewed 01/23/09