-
2133
- - Mass, Momentum, and Inertia. Inertia is the property of mass that resists
any change in motion. If an object is in
motion its inertia is often called momentum.
Momentum is equal to mass times velocity. Still another way to look at mass is that it
is the same as energy according to Einstein’s equation, where c = the speed of
light Mass = Energy / c^2
-
-------------------------------- 2133 -
Mass, Momentum, and Inertia
-
-
-
-
- What is
Mass? Mass is the volume of an object multiplied
by its density. Mass is what you
weigh. I weigh 185 pounds, which is 84
kilograms. Kilograms is a unit of force. What about when you are in outer space? You still have mass but you are weightless.
-
- The reason is
that weight is not exactly mass. Weight
is the force of gravity. And, the force
of gravity is actually the result of two masses, the product of your mass and
the mass of the Earth divided by the square of the distance between you and the
center of Earth. When you are in outer space
you still experience the force of Earth’s gravity but you are so far away the
force is very, very small.
-
----------------- Force
of Gravity = - G * m
* M / distance^2
-
- Another way
to look at mass is that it is what makes an object hard to move. The more massive an object the harder it is
to get moving. This aspect of mass is
called Inertia. Inertia is the property
of mass that resists any change in motion.
If an object is at rest it takes a force to accelerate it and get it
moving. If an object is moving it takes
an opposite force to decelerate it or to slow it down. If an object is in motion its inertia is
often called momentum. Momentum is equal
to mass times velocity.
-
------------------- Momentum
= mass * velocity
-
- But, even if
an object is not in motion it still has mass and inertia. This could be because no object in the
Universe is really “at rest”. Everything
is in motion. The Earth is rotating, the
Earth is in Orbit around the Sun, the Sun is in orbit around the Milky Way, all
the galaxies are in motion moving away from each other.
-
- The only way
you can define motion is relative to some other object. In other words, motion must have a frame of
reference. In fact, in order to measure
distance you must compare length to a frame of reference. In order to measure time you must start time
with some frame of reference. Velocity
is distance per unit time. Since both
distance and time are relative, velocity too must be relative. Your velocity depends upon your frame of
reference.
-
- So,
everything that has mass has momentum which is its mass * velocity. It was once thought that an object at rest
was its natural state. With this same
reasoning we can see that it is not “at rest” that is the natural state; it is uniform
motion that is the natural state.
-
- An object in
uniform motion tends to remain in uniform motion forever unless acted upon by
another force. It requires a force to
change the momentum of any object. The
Earth has a constant velocity of 67,108 miles per hour around the Sun. It will continue to orbit the Sun at this
speed forever unless acted upon by some other force. (Angular Momentum will be
saved for a later discussion).
-
- A force is
needed to change an object’s velocity. A
change in velocity is called acceleration.
-
- The force is
equal to the mass times the acceleration it causes. Or, mass is an object’s resistance to
acceleration.
-
-------------------- F
= m*a
-
- In other
words, force is equal to the mass times the rate of change of velocity. This is called the Inertial force. If the Inertial force and the force of
gravity are the same. Then:
-
--------------------
M * a =
G * mE * M / r^2
-
- The Inertial
mass, M, and the Gravity mass, M, are the same. So:
-
-------------------- a =
G * mE / r^2
-
- The mass of
the Earth is “mE”. “G” is the Constant
of Proportionality for Gravity that we use depending on our units of
measurement. For units in kilograms,
meters, seconds:
-
-------------------
G =
6.67 meters^3 / (sec^2 * kilograms)
-
- The
acceleration, "a", does not depend on the mass of the object. In a vacuum a feather and a hammer will fall
at the same acceleration. This was
proven by the Apollo astronaut in an experiment performed on the Moon,
remember?
-
- Still another
way to look at mass is that it is the same as energy according to Einstein’s
equation, where c = the speed of light:
-
-------------------- Mass
= Energy / c^2
-
Now, we have to ask “ What is Energy?“. Energy is the same as Work over some duration
of time. And, Work is some force
operating over a distance.
-
-------------------- The
change in Energy = work
-
-------------------- Work
= force * distance
-
-------------------- Energy
= force * distance
-
-------------------- Distance
= velocity * time
-
-------------------- Energy
= force * velocity *time
-
-------------------- Force
= mass * acceleration = mass
* velocity / time
-
-------------------- Force
is measured in: kilograms * meters
/second^2
-
-------------------- Energy = mass
* velocity * velocity
-
-------------------- Energy
is measured in: kilograms * meters^2 /
second^2
-
-------------------- Energy
= momentum * velocity
-------------------- E
= m * v^2
= m * v * v
-
- This looks a
lot like Einstein’s equation:
-
-------------------- E
= m * c^2 = m * c * c
-
- But, the only
thing that can travel at the speed of light is zero mass. Photons and all electromagnetic radiation
have zero mass. If the mass is zero, the
momentum is zero, and all that is left is pure energy traveling at the speed of
light. Something is not right here? According to the equation if mass is zero,
Energy is zero.
-
- If an object
is moving it would seem that it would have more energy than an object at
rest. Does that meant that an object
that is moving has more mass than an object at rest?
-
- Of course,
moving is always relative to an observer.
Velocity is always relative to an observer. If an observer measures a mass of an object
and they both are at rest relative to each other, the object measured is said
to have a “rest mass”. If that same mass
is now in motion at some velocity relative to the observer its mass is equal to
the rest mass divided by the square root of ( 1 - velocity^2 / speed of
light^2):
-
-------------------- Mass
= rest mass / (1 - v^2/c^2)^.5
-
- So, the mass
does change with relationship to its velocity.
Mass increases as velocity increases.
Here is a table of the changes of one kilogram of mass as the velocity
increases as a percent of the speed of light:
-
-------------------- Rest 1 kilogram
-
-------------------- 10% 1.01
-------------------- 50% 1.16
-------------------- 80% 1.93
-------------------- 90% 4.44
-------------------- 99% 31.5
-------------------- 99.99% 2,224
-------------------- 99.9999% 1,572,817 kilograms
-
-
-------------------- Force
= mass * acceleration, but only at the slower speeds.
-
-------------------- Force
= m * a + velocity * (change in mass / change in time)
- So, the force
does also change with relationship to its velocity. Force increases as mass increases as velocity
increases. As your velocity approaches
the speed of light it takes an infinite force to accelerate an infinite
mass. An impossible situation.
-
- There is no
way to measure mass that is in constant, uniform motion. A force must act on it to determine its
mass. And, there is no way to tell the
difference between the constant force of gravity and the constant force of constant
acceleration in the same direction.
-
- Like mass,
light will fall under the influence of gravity.
If this is true than the idea that light has no momentum is untrue. Light does have momentum and, therefore,
energy does have momentum.
-
- When light
falls it undergoes a frequency shift as it loses energy. This is called a gravitational redshift. The frequency of the light shifts lower, and
the wavelength of the light shifts longer.
-
- Sunlight
leaving the Sun undergoes a frequency shift of .00000212 in the ratio of the
change of frequency over the frequency:
-
-------------------- Change
of frequency / frequency = - G * Ms/ R * c^2
-
-------------------- Ms
= mass of Sun = 2 * 10^30 kilograms
-
-------------------- R
= Radius of the Sun = 7 * 10^8 meters
-
-------------------- G
= the Gravitational Constant
-
-------------------- c
= Speed of Light.
-
- As the mass
of a star, Ms, gets bigger the frequency shift gets larger. When the frequency shift gets as large as the
frequency:
-
-------------------- Change
of frequency / frequency = 1
-
- The frequency
is shifted to zero. That is, no light
leaves the gravity of the large mass.
When this happens you create a Black Hole. Not even light can escape. A Black Hole is formed when:
-
-------------------- G
* M / R * c^2 is greater than ½
-
- So, we have
concluded that light has momentum, in fact, all electromagnetic energy has
momentum. When electromagnetic waves are
absorbed or reflected they transfer momentum to that material.
-
- The rate at
which momentum is transferred per unit area is a force exerted per unit area,
which is pressure. Electromagnetic waves
exert Radiation Pressure.
-
- I am sure all of you have seen the experiment
with the black and white rotating vain inside a light bulb glass. When light is shown on the vain the black
side absorbs the radiation, and the white side reflects the radiation, and the
momentum of that radiation causes the vain to spin. Radiation pressure is real. Light does have momentum.
-
- The photons
leaving the surface of the Sun exert a Radiation Pressure. This can be illustrated by the fact that
interstellar dust does not fall into the Sun.
This interstellar dust is not orbiting the Sun it is just dispersed in
interstellar space. Yet, it does not
fall into the Sun due to the Sun’s gravity pulling it in because of solar
radiation pressure is pushing it out.
-
----------------------- The
Energy emitted by the Sun = 1.4*10^3 watts
/ meter^2
-
---------------------- The
Radiation Pressure = the Intensity of this Energy / the speed of light.
-
-------------------- Radiation
Pressure = 1.4 * 10^3 watts / m^2 / 3 * 10^8 m / sec^2
-
-------------------- Radiation
Pressure = .5 * 10^-5 kilogram / m * sec^2
-
- The radiation
pressure on a dust particle would depend on its surface area. A typical dust particle has a radius of .5 *
10^-6 meters. Its area would be
pi*radius^2. Area = 0.8* 10^-12
meters^2.
-
- The force on
the dust particle = pressure * area = (.5 * 10^-5 kilogram / m * sec^2) * (0.8* 10^-12 meters^2)
-
-------------------- Force
of Radiation = .4 * 10^-17 kg * m/ sec^2
-
- Now, we
compare this force with the force of gravity = G * m * M / R^2
-
- We need to
know the mass of the dust particle, m, and the distance from the Sun, R. Assume the distance is the same as the Earth
distance from the Sun, 1.5 * 10^11 meters.
The Density of dust is 3*10^3 kilograms/m^3. The volume of dust particle = 4/3 * pi *
radius^3. The radius is .5 * 10^-5
meters.
-
-------------------- Mass
= volume * density
-
-------------------- Mass = 4/3
* pi * (.5 * 10^-5)^3 * 3*10^3 kg/m^3
-
-------------------- Mass
of dust particle = 1.57 * 10^-15 kg
-
-------------------- Mass
of Sun =
2 *10^30 kg
-
-------------------- Distance
from the Sun = R
= 1.5*10^11 m
-
-------------------- Force
of gravity = G * m * M / R^2
-
---------------- Force
of gravity = (6.67*10^-11) * (1.57 * 10^-15)
* (2 *10^30) / (1.5*10^11) ^2
-
-------------------- Force
of gravity = .9*10^-17 kg*m/sec^2
-
-------------------- Force
of Radiation = .4*10^-17 kg*m/sec^2
-
- The two
forces are about the same so radiation pressure due to the momentum of light is
enough to balance the gravitational force of the Sun so the interstellar dust
particles remain suspended in space and do not fall into the Sun.
-
- Mass is
always conserved. It can change into
energy, but, the mass/energy total remains constant. Momentum is also conserved. Mass*velocity can change by transferring
momentum to another object, but, the total mass*velocity remains the same.
-
- It is
interesting that mass cannot be measured without some force to change its
momentum. And, the total mass/energy in
the Universe remains the same regardless of what changes. With all of these properties of mass
understood you would think that we have explained “what is mass?” But, I still do not know what causes mass to
exist in the first place.
-
- It should be
pretty simple to explain. With all of
these properties we can prove that an elephant has more mass than an ant. To explain why, we simply state, that an
elephant has more atoms than an ant. We
know the mass of each atom, about 3*10^-26 kilograms, and we count the number
of atoms. An elephant has 3*10^29 atoms.
So its mass is 10^4 kilograms ( 11 tons).
The ant has 3^10^20 atoms and only has a mass of 10^-5 kilograms (.01
grams). Ok, but what causes the mass of
an atom?
-
- Atoms are
made up of electrons, protons, and neutrons.
We simply add up the mass of these atomic particles to get the mass of
an atom:
-
-------------------- Electron
mass = .89 * 10^-30 kilograms
-
-------------------- Proton
mass =
1,670 * 10^-30 kilograms
-
-------------------- Neutron
mass =
1,670 * 10^-30 kilograms
-
- Ok, then what
causes the masses of these atomic particles?
Now, we are getting somewhere.
Everything we know, all atoms, are made up of 12 elementary particles. So, for each atom we simply add up the masses
of its elementary particles and it can’t be broken down any further than
that.
-
- Actually, it
gets simpler because the world that we actually see is made up of only four
elementary particles plus two force carrying particles. The other eight elementary particles are very
short-lived, they decay quickly into the other particles, and they barely
interact with the four particles and two forces carriers that make up our
world.
-
- Elephants and
ants, and everything else, are made up of electrons, neutrinos, up quarks and
down quarks. It turns out that every
proton is composed of two up quarks and one down quark. And, every neutron is composed of one up
quark and two down quarks.
-
- The masses of
these elementary particles are given as energy levels because it is easier to
measure. Giga electron volts are 1
billion electron volts, GeV = 10^9 eV.
And, mass is energy / c^2, E = m*c^2:
For example the proton and the neutron are each .937 GeV:
-
- GeV Kilograms
-
----------------- Electron = 5
* 10^-4 .89 * 10^-30
-
------------------ Up
Quark = 3
* 10^-3 5.4 * 10^-30
-
------------------ Down
Quark = 6 * 10^-3 1.1 * 10^-30
-
------------------ Electron
Neutrino = 1
* 10^-8 .000018 *
10^-30
-
- The neutrinos
are neutral. The electrons interact with
photons which are the force carriers for the electromagnetic force. And, gluons interact with quarks and are the
force carriers for the Weak Nuclear Force.
-
- Ok, now what
causes the masses for the 4 elementary particles? And, what about the remaining eight
particles, do we know their masses? The
masses of the second generation particles are:
-
GeV Kilograms
-
------------------ Muon = .106 189
* 10^-30
-
------------------ Charm
Quark = 1.3 2,321
* 10^-30
-
------------------ Strange
Quark = .1 179
* 10^-30
-
------------------ Muon
Neutrino = 2 * 10^-3 3.6 * 10^-30
-
- And, the
masses for the third generation particles are:
- GeV Kilograms
-
------------------ Tau = 1.7771 3,172 * 10^-30
-
------------------ Top
Quark = 175 312,389*
10^-30
-
------------------ Bottom
Quark = 4.3 7,676
* 10^-30
-
------------------ Tau
Neutrino < .02 36
* 10^-30
-
- And, that’s
it. What’s left? Well, how do these 12 elementary particles
have mass? To answer this we have to
introduce another force carrier particle that has just been discovered.
-
- This theory
was proposed by Peter Higgs and the particle is called the Higgs Boson. A Boson is any elementary particle that has
an integral spin of 1. Spin is a way of
defining a particle’s angular momentum.
Photons are Boson force carriers and they have a spin of 1. Fermions are the other elementary particles
that have a spin of ½. Electrons,
protons, and quarks are Fermions and have a spin of ½.
-
- Ok, we know
that photons are Bosons and are force carriers for the electromagnetic
force. There are other Boson force
carriers for the Weak Nuclear Force.
And, lastly there is thought to be Bosons that have a spin of zero. This is the Higgs Boson and it must have an
enormous mass:
-
- GeV Kilograms
-
---------------- Higgs
Boson > 180 321,314
* 10^-30
-
- That enormous
mass, and enormous amount of energy, is why the Higgs Boson is so difficult to
discover. It is thought to exist in the
vacuum of space. The theory is that
empty space is really not empty and not zero energy. The Higgs Bosons exist everywhere in space
just like photons exist everywhere in light.
-
- The theory holds that Higgs Bosons interact
and pull on all the other elementary particles to give them their mass. It is the pull of the Higgs Bosons that cause
particles to have inertia. The mass of
every particle comes from being pulled in space in this manner.
-
- Particle physics have been searching for the Higgs
Boson . A more powerful particle
accelerator will come on line in CERN, Switzerland having:
-
------------------ > 17 Tera eV
-
------------------ > 17,000 GeV
-
- If the Higgs
Boson particle does exist they should find it in this amount of energy. If we find it we may finally be able to
answer the question: “ What is Mass?”.
Tera eV’s should bring us a lot of new discoveries. Stay tuned.
-
--------------------------------------------------
-
- (1) Here is the relative mass of various objects
in kilograms:
Electron
10^-30 kilograms =
.0005 GeV
Hydrogen 10^-27
Oxygen
atom 3*10^-26 = 16.8
GeV
Dust 10^-15
Raindrop 10^ -6
Ant 10^-5
Elephant 10^4
Battleship 10^8
Moon 10^23
Earth
10^25
Sun
10^30
Milky
Way 10^41
Universe 10^52 This is a big number.
- (2) Joule of Energy = 6.24 * 10^18 eV
-
- October 18, 2018. 631
----------------------------------------------------------------------------------------
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--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
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--- to:
------
jamesdetrick@comcast.net
------ “Jim Detrick” -----------
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--------------------- Thursday, October 18, 2018 -------------------------
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