- 3155 - ENERGY - 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
- ----------------------- 3155 - ENERGY - 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.
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- 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.
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----------------- Force of Gravity = - G * m * M / distance^2
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- 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.
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- 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.
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------------------- Momentum = mass * velocity
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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).
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- A force is needed to change an object’s velocity. A change in velocity is called acceleration.
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- The force is equal to the mass times the acceleration it causes. Or, mass is an object’s resistance to acceleration.
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-------------------- F = m*a
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- 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:
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-------------------- M * a = G * mE * M / r^2
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- The Inertial mass, M, and the Gravity mass, M, are the same. So:
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-------------------- a = G * mE / r^2
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- 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:
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------------------- G = 6.67 meters^3 / (sec^2 * kilograms)
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- 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?
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- 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:
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-------------------- Mass = Energy / c^2
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- 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.
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-------------------- The change in Energy = work
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-------------------- Work = force * distance
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-------------------- Energy = force * distance
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-------------------- Distance = velocity * time
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-------------------- Energy = force * velocity *time
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-------------------- Force = mass * acceleration = mass * velocity / time
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-------------------- Force is measured in: kilograms * meters /second^2
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-------------------- Energy = mass * velocity * velocity
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-------------------- Energy is measured in: kilograms * meters^2 / second^2
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-------------------- Energy = momentum * velocity
-------------------- E = m * v^2 = m * v * v
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- This looks a lot like Einstein’s equation:
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-------------------- E = m * c^2 = m * c * c
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- 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.
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- 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?
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- 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”.
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- 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):
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-------------------- Mass = rest mass / (1 - v^2/c^2)^.5
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- 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:
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-------------------- Rest 1 kilogram
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-------------------- 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
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-------------------- Force = mass * acceleration, but only at the slower speeds.
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-------------------- Force = m * a + velocity * (change in mass / change in time)
- 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.
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- 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.
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- 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.
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- 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.
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- Sunlight leaving the Sun undergoes a frequency shift of .00000212 in the ratio of the change of frequency over the frequency:
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-------------------- Change of frequency / frequency = - G * Ms/ R * c^2
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-------------------- Ms = mass of Sun = 2 * 10^30 kilograms
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-------------------- R = Radius of the Sun = 7 * 10^8 meters
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-------------------- G = the Gravitational Constant
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-------------------- c = Speed of Light.
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- As the mass of a star, Ms, gets bigger the frequency shift gets larger. When the frequency shift gets as large as the frequency:
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-------------------- Change of frequency / frequency = 1
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- 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:
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-------------------- G * M / R * c^2 is greater than ½
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- 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.
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- 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.
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- 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.
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- 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.
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----------------------- The Energy emitted by the Sun = 1.4*10^3 watts / meter^2
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------------- The Radiation Pressure = the Intensity of this Energy / the speed of light.
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-------------------- Radiation Pressure = 1.4 * 10^3 watts / m^2 / 3 * 10^8 m / sec^2
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-------------------- Radiation Pressure = .5 * 10^-5 kilogram / m * sec^2
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- 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.
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- The force on the dust particle = pressure * area = (.5 * 10^-5 kilogram / m * sec^2) * (0.8* 10^-12 meters^2)
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-------------------- Force of Radiation = .4 * 10^-17 kg * m/ sec^2
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- Now, we compare this force with the force of gravity = G * m * M / R^2
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- 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.
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-------------------- Mass = volume * density
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-------------------- Mass = 4/3 * pi * (.5 * 10^-5)^3 * 3*10^3 kg/m^3
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-------------------- Mass of dust particle = 1.57 * 10^-15 kg
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-------------------- Mass of Sun = 2 *10^30 kg
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-------------------- Distance from the Sun = R = 1.5*10^11 m
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-------------------- Force of gravity = G * m * M / R^2
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---------------- Force of gravity = (6.67*10^-11) * (1.57 * 10^-15) * (2 *10^30) / (1.5*10^11) ^2
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-------------------- Force of gravity = .9*10^-17 kg*m/sec^2
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-------------------- Force of Radiation = .4*10^-17 kg*m/sec^2
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- 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.
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- 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.
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- 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.
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- 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?
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- 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:
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-------------------- Electron mass = .89 * 10^-30 kilograms
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-------------------- Proton mass = 1,670 * 10^-30 kilograms
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-------------------- Neutron mass = 1,670 * 10^-30 kilograms
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- 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.
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- 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.
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- 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.
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- 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:
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- GeV Kilograms
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----------------- Electron = 5 * 10^-4 .89 * 10^-30
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------------------ Up Quark = 3 * 10^-3 5.4 * 10^-30
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------------------ Down Quark = 6 * 10^-3 1.1 * 10^-30
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---------------- Electron Neutrino = 1 * 10^-8 .000018 * 10^-30
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- 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.
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- 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:
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- GeV Kilograms
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------------------ Muon = .106 189 * 10^-30
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------------------ Charm Quark = 1.3 2,321 * 10^-30
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------------------ Strange Quark = .1 179 * 10^-30
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------------------ Muon Neutrino = 2 * 10^-3 3.6 * 10^-30
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- And, the masses for the third generation particles are:
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- GeV Kilograms
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------------------ Tau = 1.7771 3,172 * 10^-30
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------------------ Top Quark = 175 312,389* 10^-30
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------------------ Bottom Quark = 4.3 7,676 * 10^-30
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------------------ Tau Neutrino < .02 36 * 10^-30
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- 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.
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- 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.
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- 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:
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- GeV Kilograms
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---------------- Higgs Boson > 180 321,314 * 10^-30
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- 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.
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- 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.
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- Particle physics have been searching for the Higgs Boson . A more powerful particle accelerator will come on line in CERN, Switzerland having:
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------------------ > 17 Tera eV
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------------------ > 17,000 GeV
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- 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.
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- 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.
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- Joule of Energy = 6.24 * 10^18 eV
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- May 12, 2021 ENERGY - Mass and Inertia? 631 2133 3155
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