------------ 2747 - FORCE = mass * acceleration?
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----------------------- F = m*a.
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- Newton derived an equation for this universal force of gravity between two masses as being proportional to the product of the two masses and inversely proportional to the square of the distance between them.
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------------------------ F = G* m*M / r^2
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-------------------------- G = the Universal Constant of Gravity * m*M = the product of the two masses / r ^2 = the radius, or, the distance between the centers of the two masses.
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- That the Force is inversely proportional to the square of the distance makes sense because the force spreads out like an expanding sphere. The area of the sphere grows as 4*pi*r^2. Therefore the intensity of the force is spread out, or decreases, in proportion to r^2.
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- G is determined experimentally. It is derived from the above Newton formula when the two masses are known, the distance between their centers are known, and the force of gravity is measured.
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------------------- G is then calculated. G = F*r^2/m*M
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-------------------- G = 6.67259 * 10^-11 meters^3 / kilogram * seconds^2
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--------------------------------------- FORCE:
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- But, we started out with Force = m*a. So, the Force of gravity = m*a , and , = G*m*M / r^2. Where m is your mass, for example, and M is the mass of the Earth. On the Earth surface r = the radius of the Earth. The mass, m, your mass, cancels out.
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- So, the force of gravity is the same for all bodies on the surface of the Earth. We are left with the acceleration of gravity = G*M / r^2. Substituting into this formula we calculate the acceleration of gravity to be 9.8 meters/second^2.
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------------------------- g = G*M / r^2 = 6.67259*10^-11 m^3/kg*sec^2 * 5.9742*10^24 kg / (6.378*10^6m)^2. g = 9.8 m/sec^2.
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- g = approximately 10 meters per second per second, or 32 feet per second per second. So the acceleration of gravity is the same for all objects in free fall. With no air resistance a feather and a hammer would fall to Earth at exactly the same rate.
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- If you free fall from an airplane after one second you have dropped 5 meters and reach a velocity of 10 meters per second (22 miles per hour). In two seconds you will have dropped 15 meters and have a velocity of 20 meters per second (45 mph). After 3 seconds you have fallen 25 meters and have a velocity of 30 meters per second(67 mph). After 4 seconds, 35 meters and 40 meters per second (89 mph). After 5 seconds, 45 meters and 50 meters per second 112 mph). After 6 seconds you are going 134 mph.
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- Actually air resistance will normally slow a falling body down to 120 mph maximum. Of course, you can stream line yourself and put your body in a bullet shape facing straight down and reach 200 mph, but a safer process might be to open your parachute and get more air resistance, not less.
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- Weight is often confused with mass. Actually, Weight is the force of gravity. Weight is mass * 10 meters / second^2. If you go to a different elevation, increasing your distance from the center of the Earth, your weight will change, decrease , but your mass will remain the same.
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- A Mass traveling at a constant velocity requires no Force. Constant velocity, including zero velocity (rest mass), is the natural state of all things. Any object will move at a constant velocity in a straight line forever with no force ever applied.
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- To change a velocity requires a force. And a change in velocity is called acceleration, a = dv / dt. Velocity is a change in distance over a change in time, v = dx / dt.
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- It is all relative because to record a change you must compare a beginning distance relative to an ending distance, or a start time relative to a stop time in order to record a time interval, or, change in time. Distance and length are measures of space. So, velocity is really a ratio of space and time, dx / dt.
- F = m*a gets us to the basics of physics. What is space, what is time, what is mass, what is force? These fundamental concepts have had centuries of study but we really do not fully understand them today. Sorry.
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- It takes a force to change the velocity of a mass. Therefore, we define force as a change in velocity, an acceleration of a mass, F = m*a. A bigger mass requires a bigger force to accelerate it. A bigger force is required to accelerate a mass faster.
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- Force is a vector quantity. It has both magnitude and direction. The direction is the direction of acceleration, which is also a vector quantity. Force is the product of mass and the rate of change of the rate of change of space with respect to time.
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- Rate of Change is the same as the slope of the distance curve versus time, or the first derivative, velocity = dx / dt. The rate of change of the rate of change is the slope of the velocity curve plotted versus time, or the second derivative, acceleration = d^2 x / dt^2.
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------------------- Mass times velocity is momentum, m*v = momentum.
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- Momentum is the same as inertia. Force is the rate of change of momentum,
F = d(mv) / dt. If a force moves 1 kilogram mass increasing its velocity by 1 meter/second in one second then it is defined as a force of 1 Newton. It just becomes easier to say a force of Newtons, rather that a force of kilograms*meters/second^2. But, remember these names are just for convenience the fundamentals are still mass*space / time.
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------------------------- Energy is a force acting over a distance. E = F*dx.
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- Energy = kilograms*meters^2/seconds^2, or Joules. Kinetic Energy = ½ m*v^2 One Joule of energy is a force of 1 kilogram increasing velocity 1 meter/second in 1 second over a distance of 1 meter.
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------------------------ Work is the amount of change in Energy. It is a change in force * distance and has the same units as Energy, kilograms*meters^2/seconds^2.
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- The amount of Work done is the amount of change in Energy levels over time. Work, Torque, Heat Flow are all changes in Energy measured in Joules, which is kilograms* meters^2/seconds^2.
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----------------------- Temperature for Heat Flow is converted into Energy using Boltzmann’s constant, 1.38*10^-23 Joules/Kelvin.
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- Power is the rate of doing work, or the rate of change of Energy, force * distance / time, kilograms*meters^2/seconds^3. Power is expressed in Watts, which is work done in 1 second. 1 Watt = 1 Joule /second.
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- Remember, any time we say “the rate of change“, that is the same mathematically as taking “the derivative“. It is the slope of the curve of the parameter that is changing, in this case changing versus time.
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----------------------------- MASS:
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- Ok, we are getting carried away trying to define what a FORCE is. We can say it is a push or pull that accelerates a mass, but, what is a mass?
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- Mass implies a measure of the “quantity of matter“. It comes from the Latin word meaning lump of dough, or bread. In the Catholic Church it is the Eucharistic mass that is the body of Christ. Somehow it also became the word for inertia; it takes a force to get something moving; if it is moving and has some momentum it takes an opposite force to slow it down or to stop it.
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- Mass gets defined from three different perspectives: gravity, inertia, and energy. Mass first appeared in science as “inertia mass” in the CONSERVATION OF MOMENTUM,
p = m*v and Force = the product of mass and acceleration, F = m*a.
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- The gravity aspects of mass were discussed in the above paragraphs regarding the force of gravity, or weight, being the product of mass and the acceleration of gravity, g.
Force (weight) = m * g.
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- In 1905 Einstein’s theory of relativity changed everyone’s concept of mass. E = m*c^2 meant that mass can change into energy and energy can change into mass. It also meant that mass of a body increase with its velocity, v.
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----------------------- MASS = mass at rest /(1-v^2/c^2)^.5
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- For example: If a rocket ship weighs 100 kilograms*m/sec^2 on the launch pad. Then its mass is roughly 10 kilograms with 10 meters/second^2 of acceleration of gravity. But, it the rocket is traveling at 86% the speed of light its mass is 10 kg / (1-(.86(^2).5
Mass = 20 kilograms, the mass has doubled at that velocity. Energy changes into mass.
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- It works the other way too, mass changes into energy. If a body gives off energy as radiation its mass diminishes by Energy/c^2, Energy / 90,000,000,000,000,000 meters^2/seconds^2.
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- Then Max Planck came along and said that Energy and Mass comes to us in packets, or quanta, as in Quantum Mechanics. Energy = Planck’s Constant * frequency = Planck’s Constant * c/wavelength. Planck’s Constant = h = 6.625 *10^-34 kilogram*meter^2/second.
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- Note that Planck’s Constant is a unit of Energy times time, or a unit of Action . Action = m*v*dx = m * dx * dx/dt.
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- Force = Newtons = kilograms * meters / seconds^2 = m*dx/dt^2 = dmv/dt.
Momentum = m*v = m*dx*dt.
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- Action = Force * distance * time = Newton * meters * seconds = kilograms * meters^2/second = m*dx^2/dt
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- Energy = Joules = Force * distance = kilogram*meters^2/seconds^2 = md^2x/dt^2.
Kinetic Energy = ½ m*dx/dt*dx/dt.
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- Work is the change in Energy, delta E, dw = F*dx.
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- Torque and Heat Flow are forms of Energy and have the same units.
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- Power = watts = rate of change of Energy with time = dE/dt = kilograms * meters^2/seconds^3.
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- Entropy = Energy / temperature = kilogram*meters^2/seconds^2*Kelvin
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- Now, mass is thought of as being both a particle and a wave. The momentum of a particle, m*v = Planck’s constant / wavelength, h/w.
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- Gravitational force is a function of an observer’s position as well as his velocity and acceleration, and, therefore, is a property of space-time. Distance, length, velocity, acceleration are all descriptions of space - time, and, are connected by Motion. Motion can be inferred only with reference to a second object. Motion is relative and always requires a reference.
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---------------------- SPACE: Space is a positional quality of all objects.
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- A space with 2 dimensions expands as the circumference of a circle proportional to the radius ( 2*pi*r). A space with 3 dimensions expands as the surface of a sphere which proportional to the radius squared (4*pi*r^2) If space were 4 dimensions the gravitational force would decrease proportional to the radius cubed ( 8*pi*r^3). Since Newton showed that gravity decreases as the radius squared then space must be 3 dimensions.
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- From Einstein’s perspective space is viewed as sets of spatial and time relationships among objects (mass and energy). The space -time structure is based upon the propagation of light and the motion of free-falling bodies.
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- But, free falling is not in Euclidian space it is in Riemannian space which is curved space-time and straight lines become geodesic lines, or, Great Circles on a spherical surface. Airlines travel a geodesic line between cities, the shortest distance is a great circle on the surface of the Earth.
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- Emmy Noether a mathematician who in 1932 deduced the theorem that for every continuous Symmetry in the laws of physics there exists a LAW OF CONSERVATION. Noether’s theorem is one of the most profound theories ever deduced. It is right up there with Einstein’s Theory of Relativity.
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- Space has Symmetry. It is Isotropic, it looks the same in all directions. As a consequence of the rotational symmetry of space the law of the CONSERVATION OF ANGULAR MONENTUM is derived.
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- The LAW OF CONSERVATION OF LINEAR MOMENTUM is a consequence of the translational symmetry, or, homogeneity of space. Einstein used this Theorem of Symmetry for inertia which is equivalent for all states of motion to derive the Theory of Relativity.
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- Wolfgang Pauli used Symmetry to predict the existence of the neutrino as a particle of no charge and very small mass using the CONSERVATION OF MOMENTUM. The neutrino was discovered 26 years later in 1956.
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-------------- MASS: From Gauge Symmetry physicists have deduced that space is not empty, it contains virtual particles called Higgs Bosons that attract all matter giving it inertia and mass. This is a theory of symmetry that could explain what is mass. The Higgs particle was just recently discovered in the particle accelerator at CERN, Switzerland.
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-------------- ENERGY: The fact that the laws of physics are invariant under all translations in time it follows the Law of CONSERVATION OF ENERGY. All forms of energy can be changed but they can never be destroyed in order to maintain this Symmetry.
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- Doug is driving his 1000 kilogram Cobra down a level stretch of highway going 60 miles per hour (30 meters/second). He takes his foot off the acceleration and lets the Cobra coast and times how long it takes for the Cobra to slow down to 50 miles per hour (25 meters/second). It takes 10 seconds.
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- The Kinetic Energy of the Cobra at 60 mph = ½*m*v^2 = ½*1000Kg*(30m/s)^2 = 450,000 kg*m^2/sec^2. When the Cobra slows down to 50 mph the Kinetic Energy was ½*1000kg*(25 m/s)^2 = 312,500 kg*m^2/sec^2.
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- So, in 10 seconds the Cobra lost 137,000 joules of Energy. This amounts to 13,750 joules/second, which is the same as 13,750 watts. This is equivalent to 137 100 watt light bulbs needed to keep the car going down the highway at 60 mph. (You can try this with your car and learn how much horsepower you are consuming down the highway.)
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- The energy is consumed but not lost. Energy is converted mostly into heat due to friction in the engine, friction in the tires, friction in the air resistance, but also in sound energy, heating the water in the radiator, etc.
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- There are .001341 horsepower in 1 watt. So, 18 horsepower is needed to maintain the Cobra at 60 mph. The other 432 horses are used for passing.
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- The average person consumes 2000 Calories per day. There are 4,200 Joules per Calorie so the person consumes 8,400,000 Joules of food energy every day. There are 86,400 seconds in a day.
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- So, Joules/seconds, or watts, is 97 watts. Each person burns energy at about the same rate as a 100 watt light bulb. So, the Cobra’s energy at 60 mph, is equivalent to 18 horses or 137 people.
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- If the horses were pulling he could probably get up to 15 mph, if the people were pushing barely 5 mph. Burning gas gets him to 60 mph, no problem, with energy to burn. At full power the Cobra is 336 kilowatts, equivalent to 3,356 100 watt light bulbs. You have to wear sunglasses in order to drive it.
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- So, what have we learned? FORCE = MASS* SPACE/ TIME / TIME. FORCE is the space rate of change of Energy. What is Energy? Because the laws of physics are symmetrical, they do not vary with time or space.
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- The LAWS OF CONSERVATION exist for MOMENTUM (MASS*SPACE*TIME), FOR MASS/ENERGY, FOR ELECTRIC CHARGE, OF PARITY, FOR GAUGES, FOR HIGGS FIELD, and more.
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- ENTROPY always increases, meaning everything in motion is towards randomness. What is Time? Maybe, my next review.
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- May 26, 2020 646 2747
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--------------------- Tuesday, May 26, 2020 -------------------------
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