- 3032 - KINETIC ENERGY - defined. It all starts with the law of the Conservation of Energy. It is an amazing concept that Energy can neither be created nor destroyed. Energy can only be changed from one form into another. And, the Energy created in the Big Bang is the same Energy we have today. It just got spread out quite a bit in the expansion of the Universe.
-------------- 3032 - KINETIC ENERGY - defined
- Energy has many different forms, starting with mass, in E=mc^2. But, there is heat, electricity, magnetism, chemical, nuclear, gravitational, radiation, rotational, potential and kinetic energy to name a few.
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- When Energy involves motion it is called Kinetic Energy, KE. If something moves you need a force to overcome its inertia and create its momentum with some velocity of motion.
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-------------------- Kinetic Energy = momentum * velocity.
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------------------- Momentum = mass * velocity,
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------------------- Kinetic Energy = mass * velocity^2.
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- Kinetic Energy increases with mass and with the square of the speed. If your car is going twice as fast it has four times as much Kinetic Energy, it takes four times more braking power to stop it. Braking turns Kinetic Energy into Heat Energy.
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- A force is something that moves a mass. A Force = mass * acceleration. (F = m*a).
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- Once a Force has accelerated a mass to some velocity, and the velocity remains constant, than no force is needed to keep it in motion at that velocity. A Force is only needed to “change” a velocity ,(dv/dt). Constant motion is a natural state of rest.
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- You may be resting on the couch but you are traveling 700 miles per hour around the center of Earth and 67,000 miles per hour around the Sun and 1,300,000 miles per hour with respect to the Microwave Background Radiation in space.
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- You feel none of this motion because constant motion is a state of rest. The accelerations that exist are too small for you to feel them, accept for the acceleration of gravity.
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-------------------------------- Kinetic Energy = ½ mass * velocity^2
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- There are many definitions involved in this equation. To understand it better let’s start with the definition of work. The amount of Work you do is equal to the Energy you start with minus the Energy you end with. Work is the change in energy. W = dE. Work is defined as a Force operating over a distance.
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---------------- W = F * dx.
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- Where “x” is a position and distance is a change in position, dx. Distance is also equal to velocity * time. (dx/dt*dt = dx)
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---------------- W = F * v * dt
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---------------- F = m * a
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- Acceleration is the change in velocity per unit time (a=dv/dt)
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---------------- F = m * dv / dt
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- Velocity equals the rate of change of distance with time (v=dv/dt)
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---------------- F = m * dx / dt^2
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---------------- W = F * dx
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---------------- W = m * dx^2 / dt^2
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---------------- W = dE = m * v^2
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--------------- Kinetic Energy = ½ m * v^2
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- The ½ gets into the equation when you treat these equations correctly as differential equations. I have over simplified the math just to show the relationships between the definitions of Work, Force, and Energy.
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- This equation for Kinetic Energy only works in our familiar surroundings. When the velocity gets very large, approaching the speed of light, the equation changes. Also, when the mass gets very small, approaching the atomic scale, the equation changes.
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- When you deal with atomic masses you run into Quantum Mechanics, that energy and light exist in quanta and are not continuous. Also, that particles and waves become inseparable.
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- Ultimately, mass and energy are the same thing and they are related by E = m*c^2.
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----------------------- Energy = mass * velocity^2
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----------------------- Energy = mass * velocity * distance / time
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----------------------- Energy = momentum * distance / time
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----------------------- Action is defined as momentum moved over some distance.
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----------------------- Energy = Action / time
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----------------------- Action = Energy * time
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- When you deal with atomic masses and the particle/wave duality you find that the Energy in a Wave is proportional to the frequency of the wave. (Energy is also inversely proportional to the wavelength of the wave).
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- And, you find there is minimum quantum of action that can not be reduced.
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- The minimum in called Planck’s Constant of Action (h) and it = 6.6^10^-34 kilogram * meters^2/ seconds.
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- Note that the units for Action are Energy * time = mass * velocity ^2* time = kilograms * meters^2 / second.
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------------------ The kinetic energy of radiation becomes:
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----------------- E = 6.6*10^-34 * frequency.
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----------------- E = h*f
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- Kinetic Energy has to account for the Theory of Relativity when velocity approaches the speed of light. The Work expended to accelerate a mass from rest to a relativistic speed :
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--------- Kinetic Energy = mc^2/ ( 1-(v/c)^2)0.5 - mc^2
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----------- Kinetic Energy can be found by subtracting the rest mass-energy from the Total Energy. If the speed is a little slower than Kinetic Energy can be approximated by the first few terms in the Taylor Series expansion of this equation:
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------------ Kinetic Energy = mc^2 + ½ mv^2 + 3/8 m* v^4/c^2 + ………
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- The concepts of momentum, energy and mass begin to merge into the Theory of Relativity and mass and energy become one and the same thing.
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- Any Work requires Energy and Energy always tries to get into equilibrium of maximum randomness, called “Entropy“. If the Sun did not continually add its energy to our planet we would continually decay into this randomness. No work could get done.
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------------------- We owe a lot to the Sun, our star in the heavens.
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February 6, 2021 KINETIC ENERGY defined 859 3032
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--------------------- --- Sunday, February 7, 2021 ---------------------------
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