Transcript Lesson 11x - MrLaFazia.com

PHY111: Summer 201253
Lesson 11: Linear Mechanics I
-
Types of forces
Inertia (Galileo)
Newton’s Laws of Motion
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Types of Forces
Below I have made a simple tree of forces. It leaves out some (pun intended, get it?), certainly,
but for you these are the ones most likely to come up. I will briefly go through each one and
discuss their basic natures.
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Types of Forces
Distance forces versus Contact forces
These are two very important force categories. It is necessary for you to know that some
forces require contact between two objects in order to act, while some can act over long
distances (through empty space, essentially). It is usually useful to demonstrate how distance
forces can act when two objects are not even in contact. Here are two examples:
1) Drop a ball. Why did it drop (what force caused this ball to change its motion)? The force
due to gravity caused the ball to change its motion.
2) Rub a balloon across your hair to produce a state of static electricity. Hold the balloon
above (but not touching) your arm-hairs or the head-hair of a peer (or even a small piece of
paper). You will observe a change in motion of the hair (or small piece of paper). Why did
the object move (what force caused this object to move)? An electric force was acting on the
hairs/paper.
In this last experiment, it is sometimes interesting to note that the electric force had to first
overcome the gravitational force in order to lift up on the object (this is most easily discussed
when the object is that small piece of paper). I have emphasized that the piece of paper
should be SMALL because of this very same "tug-of-war" between the two forces in this
vertically-oriented experiment.
If you think THAT was a mouthful,
you ain’t seen nothin’ yet.
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Types of Forces
Gravitational force
Gravity is. We do not know WHY gravity exists, but we can certainly study its effects.
Basically, anything at all that has mass has some "gravitational field" associated with it. Even
the particles of air that we breathe or that zoom by us exert a gravitational force on all other
objects. The closer two objects are, the stronger the "Weight" (or force because of gravity)
between them (and vice versa for being further away).
[For our purposes, this is governed by a "complex" instead of a "simple" relationship...in
other words the relationship between distance and gravity is non-linear].
Usually in the classroom experience we talk about gravity acting "downward," but of course
since EVERY object has its own gravitational attraction then gravity acts in whatever direction
the mass occupies. The reason we identify "down" as being toward the center of the Earth is
because the Earth's mass "trumps" the masses of any other in the area. All of the other
gravitational force sources are incredibly weak compared to the Earth (again, simply because
gravity is associated with mass, and the Earth is rather massive).
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Types of Forces
Electromagnetic forces
People tend to have fun with magnetic forces very early on in life (generally speaking). We
usually divorce magnetism from electric concepts, but the two by nature go hand in hand. It
is usually sufficient, however, to simply say that the two are very closely related and then
consider them two separate ideas on their own. Both electricity and magnetism are related
to charges. Charges make up the basics of matter. I am not going to go into a long
explanation of how magnets work (or how to make a magnet). Instead, I simply want to
point out that the Electric Force is key to understanding what is happening on the SMALL
SCALE. The Electric Force acts very much like a spring between particles.
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Types of Forces
Tension
Tension is basically the "I WANT TO STAY AS I AM!" force. If you pull on a rope, the material
of the rope resists stretching. This allows a force applied at one end to "translate" through
the rope to the other end. You can see how important it is to use rigid materials by simply
using a weak rubber band and attaching a heavy mass to the end. Then, bob the mass up
and down on the end of the rubber band. There is a definite delay in the motion due to the
ability of the rubber band to stretch. Although this IS an example of tension, for materials
like rubber bands we more correctly consider this to be a "spring force" (see an upcoming
slide). Tension can be summed up as the resistance of any material to undergo a change in its
[dimensional] characteristics. In other words, the rope did not want to lengthen (or become
thinner). If you pull on someone's hair, the same thing is seen. The strand of hair resists a
change in its dimensions and the root of the hair feels the same force as that which was
applied at the other end.
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Types of Forces
Friction
Friction is a broad category, but I typically like to break it up into two: kinetic (or sliding) and
static. Friction is most definitely a contact force. Friction exists because of microscopic
interactions between two objects' surfaces. With static friction, there must be some applied
force for these interactions to resist. If there is no force applied to try to get the object
moving, then there need be no friction! Friction's "job" is to prevent slipping (as best it can),
so if there is no danger of slippage (no force applied to resist) then a frictional force cannot
exist at that time. However, once you try to move something (applying a force), then a
frictional force because of these microscopic interactions between the two surfaces will exert
itself in the opposite direction.
If you push (or pull) hard enough, then you break those microscopic interactions between the
two surfaces and the object begins to move. The interactions are still present, but in a
weakened form. They will not return to their original strength again unless the object stops
moving across the surface (even if only for the briefest of moments). This friction while two
objects are sliding across each other is called, appropriately, sliding friction (or kinetic
friction).
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Types of Forces
Spring force
A spring (or a piece of elastic, or an air-filled ball, or a rubber band, &tc.) will resist a change
in its shape. However, it's generally not all that good at it. The force required to stretch or
compress an elastic material increases "simply" (i.e., "linearly") the further you stretch or
compress it! For instance, let us say that I take a spring. I stretch it 2 cm and I note (with a
scale) that this requires 8 Newtons of force. I then stretch it to 4 cm and note that this
requires 16 Newtons of force. My prediction is that if I stretch it to 8 cm, then it would take
32 Newtons of force to do so.
[Note that, in reality, there is always an "elastic limit." In other words, materials have an
extreme point which shows that they are actually breakable...but within the reasonable
range for any material, this "simple" relationship holds true very well].
Actual Guiness
World Record
Winner for Most
Elastic Mouth!
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Types of Forces
Air Resistance
I will be brief with air resistance. Basically, air resistance is a complicated set of
interactions...but for our purposes it can be simplified. Assume that all air is made of tiny
bowling balls. As an object moves through the air, it is continually colliding with these
extremely small bowling balls. Yes, the balls are moved out of the way or around the edges
of an object, but they take their toll on the kinetic energy. In fact, they receive some of the
kinetic energy of the moving object. That is air resistance in a nutshell.
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Types of Forces
Supporting Force
The Support force (or "Normal force," if you prefer) is the "STAY OUT OF MY SPACE!" force.
As has already been stated, materials do not like to change their characteristics. If you stand
on a floor, you are trying to compress (or at least displace) the material of the floor.
However, because of the properties of the material of the floor, it is able to resist any
significant change in its shape. This resistance is the "support force.“ The same thing is true
of leaning against a wall, or banging your head against a test paper (or desk, if you prefer).
We are very fortunate that objects can exert this support force. How well an object (or
surface) does this depends on the microscopic characteristics of the materials of which it is
made.
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Types of Forces
Applied Force
This list would not be sufficient if I left out "Applied Force.“ This pretty much covers any
other push or pull force for which your situation might call. There is not much to say about
this type, except that it is convenient to use the name. This is a very versatile force type-almost a category of its own that can (let's be honest) get you out of many "jambs" in your
work.
It is similar to me saying “Force-LaFazia” to mean “Force applied by Mr. LaFazia.”
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Galileo Galilei on Inertia
a MrLaFazia.com original snapshot
NOTE:
Galileo lived
from 1564 to
1642… NOT
1489!
SOURCE: http://www.cartoonstock.com/newscartoons/cartoonists/bro/lowres/bron1636l.jpg
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Introduction & Overview
• Galileo’s life teaches us many things
– (not the least of which is—DON’T STARE AT THE
SUN THROUGH A TELESCOPE!)
• For today, however, we will discuss his ideas
on MOTION
1) the Leaning Tower of Pisa
2) defining Force and the role of friction
3) Inertia (ramp experiments)
IMPORTANT NOTE: You will only be able to view the embedded videos by (instead) going to the
appropriate folder in the Course Documents section on Blackboard. You may have to save the videos to
your computer in order to view them.
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VIEW VIDEO CLIP HERE:
http://mrlafazia.com/studentaccess/PHY111_temp/leaning_tower.wmv
The Leaning Tower of Pisa
• This tower portion is considered “legend,” of course…but...
• Wherever he dropped the objects, Galileo showed that less
massive objects fall at the same rate as more massive ones
– air resistance must either be equal or eliminated
SOURCE: http://improbable.com/airchives/paperair/volume15/v15i3/v15i3-webimages/KIM-Galileo_of_the_lem_opt.jpeg
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Defining “Force”
• Forces are most simply defined as
SOURCE:
http://goozydumps.
files.wordpress.com
/2008/09/galileos_
experiment.jpg
– A PUSH
– Or A PULL
• It was once believed that forces were needed to KEEP
objects in motion.
– People believed this because life taught them that objects slow
down and eventually stop (like your car not moving) unless a
force keeps them going.
• Galileo showed that objects need no force to maintain their
motion.
– What people originally had not realized was the fact that friction
is a FORCE as well!
• The fact is: Forces that aren’t balanced out will ALWAYS
cause a change in any object’s motion (whether speeding
up or slowing down or changing direction)!
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VIEW VIDEO CLIP HERE:
http://mrlafazia.com/studentaccess/PHY111_temp/Galileo_ramps.wmv
Inertia
• Galileo did a number of experiments to test
his theories of forces and motion:
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SOURCE:
http://www.cartoonstock.com/cartoonview.as
p?catref=mhen235
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Inertia
• Imagine if a ball were allowed to roll down a
ramp and roll right onto a level ramp.
– Without a force to slow it down or speed it up,
what would happen to its motion?
• THIS is the concept of “inertia.”
– What would be needed to speed up the ball?
– What would be needed to slow down the ball?
– ______________
Frictional Forces slow down the ball in the real
world. This does NOT violate the concept of
Inertia, but rather justifies it!
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VIEW VIDEO CLIP HERE:
http://mrlafazia.com/studentaccess/PHY111_temp/Law%20of%20Inertia.wmv
The Law of Inertia
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Forces…Motion…& Energy?
• Do the results of the ramp experiments (see page
32, Figure 3.4 of Conceptual Physics) match up
with our understanding of the Conservation of
Energy (“Total Energy is Boring”) Principle?
• Perhaps you have heard the formation of these
concepts attributed to Sir Isaac Newton or
another scientist, before. There is a somedayfamous poem which describes this misconception
quite well. I will read it to you during our next
class…
• STAY TUNED!
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A Final Bit of Humor
SOURCE:
http://emdashes.com/assets_c/201
0/04/Galileoroll2-thumb182x224.png
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Newton’s Laws of Motion
- an introduction -
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First off, we must ask…
“What ARE Forces”??
• Put simply, a Force is “a push or a pull”.
• Looking at the BIG PICTURE, a Force is defined
as “a way to transfer Energy”.
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Vector or Scalar??
• Strictly speaking, Forces are VECTORS
• For this reason, we represent Forces with
arrows. The longer the arrow, the greater the
magnitude (number-value), and the angle of
the arrow tells us the direction of the Force!
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F.B.D.-ing
• This is best seen by drawing a Free-Body
Diagram (as important as Dimensional
Analysis!)
• A Free-Body Diagram (or FBD) is a tool that
takes an object all by itself and shows ONLY
the Forces acting on THAT OBJECT!
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An Example of FBD-ing
Box being pushed along rough surface:
N
fk
Fpush
Fg
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Why do we need to know about Newton’s
Laws of Motion???
• Newton’s 3 Laws of Motion help us to
understand WHY an object moves (or why one
doesn’t move).
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Law # 1
• The Law of Inertia
– What is inertia??
Inertia is a property of mass.
• Bill Nye says…?
• Definition (the tendency of….)
The tendency of an object to
resist a change in its motion.
• So…what IS Newton’s 1st Law of Motion??
– “An object in motion will tend to stay in motion,
and an object at rest will tend to stay at rest,
unless acted upon by an outside, unbalanced
Force.”
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Law #2
• “The acceleration an object experiences is directly
proportional to the overall Force acting on it and
inversely proportional to the object’s mass.”
• This is hard to picture, so let’s just remember it as an
equation:
F = m∙a
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Law #3
• …often known as the “action/reaction” Law
• “For every action there is an equal and opposite
reaction.”
– Examples: “Normal” force from floor, pushing against a
wall, letting air out of a balloon, &tc.
• Note: “Normal” means “Perpendicular” or “Orthogonal”. Never
think of it as the “regular” force.
Sometimes it is useful to refer to this as a “Support”
force. The two are interchangeable.
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Video Clips
• Watch Julius Sumner Miller Inertia mini-lecture
Part 1
http://www.youtube.com/watch?v=BwkUNrSCNMg
• Watch Julius Sumner Miller Inertia mini-lecture
Part 2
http://www.youtube.com/watch?v=Hyw9uNF4nmE&feature=related
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Grades/Assignments:
Read Sections 3.8-3.10; 4.6.
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Looking Ahead:
Lesson 12 will take place in-class (Room 144, this time,
remember). We will continue our discussion of Linear
Mechanics.
I will be updating both Blackboard and MrLaFazia.com for the
remainder of the semester, so that no one is inconvenienced
by the switch if they preferred Blackboard. For everyone else,
however, I will continue to develop our alternative form (as I
plan to use this full-time starting in the Fall).
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