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|Re: Speed Of X.
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Posted by morgoth/">morgoth on November 14, 1998 18:27:28 UTC
Wondering? wrote a whole load of bad physics.
First, speed is the measure of how long something takes to move from a to b in time t.
s=(a-b)/t and has units m per second or km s^-1.
Speed is a scalar as you don't specify direction, it is one dimensional.
Velocity is speed of something in a direction. Direction involves 3 dimensions so Velocity is a vector quantity.
v_ = ax_ +by_ +cz_
The _ should be written under the character and represents a BOLD character, which is how vectors are written. x_ , y_ , z_ are unit vectors representing the axes of a 3-dimensional, cartesian graph.
In this notation s=|v_ | = sqrt (a^2 + b^2 + c^2), which is simply pythagorases theorem.
Second. The momentum of an object is given as
p=m * v_ , its mass m times the velocity of an object.
Third. Acceleration is the rate of change of speed
a=s_1 - s_2 which is better written as a vector,
a_ = dv_ / dt
Fourth. Force is that which makes an object accelerate. It is the rate of change of momentum in the time it takes to change the momentum,
F=m dv_ /dt.
and as a= dv_ / dt
F=ma. Force has units km s^-2 g which is commonly called a Newton.
Fifth. Energy is that which is created or expended when a force acts. It is the sum of forces felt by an object.
E= integral ( F dt) = m * integral dv_ * dt/dt
E= m * integral (dv_) = mv^2 / 2 or a half mv squared.
E has units g m^2 commonly called a Watt.
Energy does not equal force E=F is a nonsensical statement.
In the above there is no limit to the velocity v_ that you can have. Which means that a force acting for long enough can create infinite energy. So a rocket with infinite fuel can go as fast as it wants.
Einsteins special relativity says there is an upper limit to your velocity. That upper limit is the speed of light, c. This upper limit is not chosen arbitralily, it was measured by Michelson and Morley in a famous experiment. This led to a strange result that,
E=mc^2, energy equals mass times the speed of light squared.
So what does that mean. A Mass m has an energy E that is E=mc^2. So a 1 kg bag of sugar as enough energy in it to equal a very large nuclear explosion. Nuclear weapons would not work if this principle did not hold. The mass of the Uranium in the bomb is turned into energy. Only about 2-3% of the total mass of a nuclear bomb is turned into energy. It is that energy we see as an explosion.
If any one thinks that E=mc^2 is nonsense I suggest you visit Hiroshima in Japan and see a real life example of this equation in action.
Our Sun would not work without this one equation. The mass of hydrogen atoms colliding with each other creates energy, some of that energy is turned into mass, subatomic particles called neutrinos. Some of the energy is turned into light. The light you see around you is a direct result of this equation.
Why is it this way? It just is. There is no need for a divine creator. We are, the universe is, nothing else matters.
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