Download physical science: force and motion I

http://www.nearingzero.net (labinitio035.jpg)
The Grand Unification Theory…
The idea of a GUT
seems to attract many
people who think they
can explain it all.
Naturally, when their
ideas don’t get accepted,
it’s because of some
grand conspiracy against
them.
http://ffden2.phys.uaf.edu/211.web.stuff
/Lichtenberger/main.htm
Keep that in mind while
browsing the web.
Actually, the electromagnetic and weak forces have been
shown to be different manifestations of the electroweak
force...
…so you might be justified in saying there are only three
fundamental forces in nature...
…but for now let’s say our four forces are all that are needed
to explain the universe as we know it. There are no more or
no less.
Don't let anyone invent some new force with a fancy name
and get you to invest in his (or her) new invention which will
revolutionize the world. All it will do is suck up your money.
About 1986, some distinguished physicists thought they had
found experiments which necessitated a fifth force. To
understand their work, we need to revisit the idea of mass…
If you Google “fifth force,” beware of pseudoscience gibberish.
What is mass?
The “thing” that goes into F=ma?
The “thing” that goes into F = Gm1m2/r2?
Are these two “things” (inertial mass and gravitational mass)
the same?
OR! Is there even a theoretical or experimental basis for
demanding they are the same?
Hungarian physicist, Lorand Eötvös, carried
out precise experiments between 1906 and
1909 to compare gravitational and inertial
mass.
He concluded the two were the same to
within 1 or 2 parts in 200,000,000.
A 1964 experiment1 showed the two were the same to within
1 part in 100,000,000,000.
1. P. G. Roll, R. Krotkov, R. H. Dicke, Annals of Physics, New York, 26, 442, 1964.
This experimental result is the basis for one of the postulates
of general relativity:
The Principle of Equivalence: an observer in a closed
laboratory cannot distinguish between the effects produced by
a gravitational field and those produced by an acceleration of
the laboratory.
force
a=g
uniform upward
acceleration = g
uniform gravitational
field, downwards
w = mg
“The original Eötvös experiment was designed to measure the
ratio of the gravitational mass to the inertial mass of different
substances.”
“Eötvös found the ratio to be one, to within approximately one
part in a million.”
“Fischbach and his collaborators reanalyzed1 Eötvös' data and
found a composition dependent effect, which they interpreted
as evidence for a Fifth Force.”
What do you think of this?
Remember: right now we believe there are only four
fundamental forces: strong, weak, E&M, and gravitational.
1. E. Fischbach et al., Phys. Rev. Letters, 56, 2424, 2426, 1986; E. Fischbach,
D. Sudarsky, A. Szafer, C. Talmadge, S. H. Aronson, 57, 1959, 1986.
Quotes from http://plato.stanford.edu/entries/physics-experiment/notes.html#A4-1.
Here’s some of the data supporting the fifth force. I’ll discuss
this in class.
“Fischbach and his collaborators reanalyzed1 Eötvös' data and
found a composition dependent effect, which they interpreted
as evidence for a Fifth Force.”
If this is true, two 1-kilogram masses of copper attract each
other with a different force than two 1-kilogram masses of
aluminum!
Revolutionary! Instant Nobel Prize (on confirmation)! Your
name goes down in the annals of physics next to Newton,
Maxwell, and Einstein!
Two experiments carried out in 1987 gave conflicting results:
one for the fifth force, one against it.
What’s a responsible physicist to do?
Suspend judgment until experiment (supported by theory)
offers conclusive evidence.
Ultimately, many experiments were carried out and (eventually)
demonstrated conclusively that there is no fifth force.
In the reanalysis of the Eötvös
experiment, a trend in the data
which suggested the fifth force
turned out to be a result of
statistical fluctuations. The data
had a trend, but it was accidental
and statistically insignificant.
Physics works!
Interesting discussion: http://plato.stanford.edu/entries/physics-experiment/app4.html.
The Fifth Force affair was great fun and led to a lot of nice
research grants, but in the end, there was no fifth force.
Most of us believe that four forces are all that are needed, but
because we have seen remarkable new discoveries, we are
willing to send a few of our colleagues off to search for an
experiment which demands a fifth force.
If you can show that five forces are needed to explain the
universe, I guarantee that you will win a Nobel prize. Please
remember me when you cash the check.
If you can show that less than four forces are needed to
explain the universe (i.e., that two or more forces are really
manifestations of a single force which we do not presently
understand in detail) then I also guarantee that you will win a
Nobel prize. Good luck, and remember me when you cash that
check.
Physical Science:
Newton’s Laws
“Classical mechanics” is based on Newton's three laws. These
three laws are based on experimental observations which
allow us to infer equations which we use to explain and predict
how systems respond to forces.
We can use these Newton’s laws and their equations to predict
observations which have never been made before. That's why
we believe them.
You can't "prove" Newton's laws, but you can
postulate them and see that they work.
“One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely
certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of
being overthrown by newly discovered facts. .”—A. Einstein
Here are the three laws…
On second thought, why don’t you write on a piece of paper,
to the best of your knowledge, what you believe Newton’s
three laws to be. You can use words or equations. Put your
name on the “Newton’s Laws” paper so I can use it to take
today’s attendance.
The first law is the law of inertia. It says that if no forces act
on an object, its velocity remains constant. A moving body will
keep moving and a body at rest will remain at rest.
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/newtlaws/cci.html
Let me illustrate by pushing a book across the table.
After I stop pushing on it, what happens?
It comes to rest. Its velocity changes.
What can you infer?
Forces must have been acting on it.
What was/were the force(s)?
Friction.
If no forces act on an object, its velocity remains constant.
What did it take to get the book moving?
A force.
What did the force cause?
Acceleration.
This brings us to Newton's second law. This is a nonmathematical course, so I'll first put this law in words.
When a force is applied to an object, the force changes the
body's velocity. The bigger the force, the bigger the change in
velocity. The force can be applied to make the body speed up
(gas pedal) or slow down (brakes).
A force applied to an object changes the object’s velocity.
Acceleration—the physicist’s term for change of velocity—can
be either positive or negative, and can lead to greater
velocities (“acceleration”) or smaller velocities (“deceleration”).
It’s not necessarily the
“acceleration” that hurts.
Only two of the cars are accelerating (after they have started)
…and the red car is not one of them!
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/kinema/acceln.html
Mass is a measure of the resistance of a body
to being accelerated. The greater a mass, the
more difficult it is to accelerate it.
My previous Physics 6 class liked the Pig, so it gets an encore.
Mathematically, Newton's second law says F=ma.
If you double the force on a given mass, you double its
acceleration: 2F=m(2a).
If you double the mass of an object, you double the force
needed to produce a given acceleration: 2F=(2m)a.
F=ma
kgm/s2
kilograms
meters/second2
The units of force are kgm/s2. One newton is one kgm/s2.
If I pushed on you with a force of one newton, what would
you feel?
If I tossed you a 1 kg mass, what would it feel like?
The acceleration due to gravity near the surface of the earth is
9.8 km/s2, so a 1 kg mass has a weight of 9.8 newtons, or
about 2.2 pounds.
Gravity is a force, right? That means gravity produces an
acceleration. We even talk about the acceleration due to
gravity. Why don't we feel that acceleration?
The answer is we feel the force of
gravity, every day, all the time. We call
it "weight." Weight is the force with
which gravity is pulling on us.
If forces produce accelerations, why don't we accelerate?
The answer is we do, until we come in
contact with the earth. This leads us to
Newton's third law, which says "for every
action there is an equal and opposite
reaction."
In Newton’s writings, “action” and
“reaction” refer to forces.
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1d.html
For every action there is an equal and opposite reaction.
For every action there is an equal and opposite reaction.
What does that mean? I have 9-year old twin
boys (well, they were 9 the first time* I taught
this class). When one gets mad and slugs the
other, the other slugs back.
(Don't worry, they know how to slug without hurting. Makes a
big noise so their mom yells, but nobody gets hurt.) Is that
what Newton meant by "equal and opposite reaction?"
*Helps me keep track of when I originally wrote these notes!
Of course not; you know that. A "reaction"
is a force. The figure to the right shows
what Newton's third law means.
The person is standing on the ground. The
person is pushing down on the ground
with a force equal to his weight. Newton's
third law says the ground is pushing back
on the person with a force equal to the
person's weight.
These two forces are known as an action-reaction pair. If I
push you and you fall down, that is not the action-reaction
that Newton's third law talks about. The two forces shown in
the original figure are not action-reaction forces.
Think about this: the earth is pulling on
the person, right? That's what is giving
him his weight. According to Newton's
third law, he must be pulling back on the
earth with a force equal to his weight.
Watch and I'll demonstrate...
When I jump (or drop a book if I don’t have what it takes to
jump), you don't see the earth move up to meet me (or the
book), because the earth is so much more massive than the
book. But the book and I really do pull on the earth.
Newton's second law is extremely
powerful. You can solve an incredible
number of real-world problems using it
and the third law.
According to these laws, if an object is at rest, it has no net
forces acting on it. You can use this fact to calculate
“everything” you need to know about a system of objects at
rest (or moving with a constant velocity).
I hope that the engineer who designed
your house knows his (her) physics!
A walkway at the Hyatt Regency collapsed because an
engineer didn’t double-check a simple physics calculation.
If an object is moving or accelerating,
you can use Newton's laws to calculate
(in principle) everything you need to
know about the motion of the object.
Figure taken from
http://hyperphysics.phy-astr.gsu.edu/hbase/incpl2.html#c1.
I paid for use of material on this site
A nonzero acceleration means there is a net nonzero force
acting on the object.
upward force of road
air
resistance
constant
velocity
other
friction
forces
weight
forward force of
road on tires
A moving but not accelerating object probably has a number
of forces acting on it, because in the real world there is almost
always friction present. If an object is moving with a constant
speed and has friction trying to slow it down, some other force
must be applied to counteract the friction. (Where is the
“engine force?”)
Here's an interesting problem to consider. You are in a car
going around a curve at a constant speed. Are there any net
(unbalanced) forces acting on you? Are you being
accelerated? If yes, what is causing the acceleration?
road force
http://136.142.138
.22/CARS.HTM
The force of the road on the tires causes an acceleration
directed towards the “center of curvature.”
This is all pretty dry stuff. Let's do a little experiment on
forces. Hopefully this experiment will not dampen our spirits...
The little demonstration illustrates a number of important
features of physics problem-solving.
It is critical to focus on the important things in the problem,
and ignore those things which are not important (after doublechecking that they really are unimportant).
What do you believe I think is the important thing in this
demonstration?
If you took a physics class with math and problem-solving, you
would first draw a picture of your problem, so let’s do that…
Skip to this slide if do diagram on board.
air pressure
air pressure
weight of water
weight of card
First the important thing—the card!
Next, show all the forces acting on the card.
Any other forces? If not, looks like I was in trouble!
air pressure
air pressure
weight of water
weight of card
A “sticking force” between wet card and glass jar?
Maybe a tiny one. Not big enough to show in the diagram.
“Suction” due to an air bubble in the jar?
No, no, no! Vacuums do not suck! Plus air is not a vacuum.
air pressure
air pressure
weight of water
weight of card
Oh, I almost forgot. The glass jar is touching the top surface
of the card. It could be pushing down on the card.
That doesn’t help, does it?
air pressure
air pressure
weight of water
weight of card
Come on, Physics, help us out… the card doesn’t accelerate.
Newton says the up and down arrows must balance. Air
pressure!
Air pressure! There is more “underneath” card surface for the
air to push up on than there is “above” card surface for the air
to push down on.
air pressure
air pressure
weight of water
weight of card
In fact, the upward force of the air is very large, and the glass
jar pushes down with a big force in order to balance the air
force.
If all goes according to plan, the upward and downward forces
balance, and I am “happy.”
Some interesting facts: there is enough air
pressure to hold up a 34 foot high column of
water, or about a 30 inch (960 millimeter)
high column of mercury
You couldn't get a straw more than 34 feet long (vertically) to
work, because you rely on air pressure to push the liquid up
the straw. Nor could you rely on air pressure alone to lift water
more than 34 feet up from a well.
I need to revisit the subject of mass for a bit…
Here's something to think about. How do you measure mass?
I expect most answers will involve some kind of
a balance or scale. Spring scales use a spring to
balance your weight. Would a spring scale work
on the moon? Yes, but not accurately.
Please visit howstuffworks.com
to see how lots of stuff works.
Would a spring scale work in outer space? No.
Some of you may have thought of a balance scale. The
simplest kind works like the one you saw in the first lecture:
Two identical pans, identical distances from
“hanging” point. Put unknown mass in one
pan, knowns in the other pan until balance
is achieved.
Triple beam balances are more complex, but still rely on
balancing known masses against unknown masses.
Would either of these balances work on the moon?
Yes, and accurately.
Would either of these balances work in outer space?
No! Why not?
How would you measure mass in outer space? You'd have to
use Newton's second law and some device that measures the
acceleration of an unknown mass as a result of a known force.
Such an instrument is called an inertial balance, and works in
space.
Two NASA inertial balance designs (the pictures were “live” links).
This brings up an interesting question: is the mass that
responds to gravity the same as the mass that accelerates in
response to forces?
A while back we investigated the difference between inertial
and gravitational mass, and I concluded there is currently no
conclusive evidence to suggest they are different.
All those who are non-science majors, temporarily move to the
front three rows of the room, and all those who are science
majors, move to the back of the room.
Science majors: take a little break.
Non-science majors: after a few minutes of discussion, give
me a technical term in your one of your fields that you would
like to have the science majors attempt to define.
There are two more subjects I want to cover in this discussion
of forces and motion: momentum and density.
What does momentum mean to you?
Guess what? Non-science majors get to write your definition of
momentum on a piece of paper and turn it in for today’s
attendance.
Science majors, please define the term that the non-science
majors have chosen. Turn in your definition for today’s
attendance.
Expect to get to about here.
Momentum is related to the "mass in motion part" of Newton's
first law. Remember, that law says an object in motion
remains in motion unless acted on by external forces.
Momentum is a measure of a body's "desire" to remain in
motion.
In physics, momentum is calculated using the equation p=mv.
(I guess since m was already used for mass, "p" is as good a
symbol as any for momentum.) The more mass you have, or
the faster you are going, the greater your momentum.
There is an important law of physics, known as the Law of
Conservation of Momentum. This law says that momentum is
conserved in any process, as long as no external forces are
acting.
If your car and an 18-wheeler collide, what does the Law of
Conservation of Momentum have to say?
graphics from http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/
It has been observed experimentally and verified over and
over that in the absence of external forces, the total
momentum of a system remains constant.
The above is a verbal expression of the Law of Conservation
of Momentum.
It sounds like an experimental observation, which it is…
…which implies maybe we just haven’t done careful
enough experiments, and that maybe some day we will
find the “law” is not true after all.
But the Law of Conservation of Momentum is much more
fundamental than just an experimental observation.
In 1905, mathematician Emmy Noether proved the
following theorem:
For every continuous symmetry of the laws of physics, there
must exist a conservation law.
For every conservation law, there must exist a continuous
symmetry.
The laws of physics are invariant under coordinate
transformations.
That’s a fancy way of saying you and I can pick different
coordinate systems for measurements and experiments, but
we will still arrive at equivalent results.
If the laws of physics were not invariant under coordinate
transformations, then everybody would have his own version
of the laws of physics.
Not much point in doing physics, if that’s true!
The Law of Conservation of Momentum is a mathematical
consequence of the invariance of the laws of physics under
coordinate transformations.
Any violation of the Law of Conservation of Momentum would
be as revolutionary (if not more so) as Einstein’s relativity.
But even if a violation were found, any “new” laws of physics
would contain all our “old” ones, which would still work under
“normal” circumstances.
Conservation laws are fundamental, powerful, and beautiful.
We will see another
one soon.
In contrast, Newton’s laws work only in the macroscopic
world, and are only an approximate description of nature.
Before I leave momentum, have you ever thought of racing a
train across the crossing?
What is your car’s mass? How far does it take you to stop your
car when you are going 60 miles per hour?
Some of the distance traveled is due to your reaction time, and
the rest is due to the time needed from the frictional forces
applied by your brakes to "use up" your car's momentum.
What is a train’s mass? How far does a train traveling at 60
miles per hour go before the friction forces from its brakes
cause it to stop?