re: energy producing experiments

[sm0ky2]

Im sure you have pulleys, ropes, wood, etc. wherever you are
This shouldn't be hard to build a series of mechanisms to demonstrate
everything we are discussing here.


It is not the math and theory we are after


It is Energy Producing Experiments


A Lever, the top of the short end is placed at "0"
the Atwood has an H of the large weight, directly above the short end


The long end connects to a chain


Another lever, that when it is fully activated, the long end sits at the
just higher than the bottom of the smaller weight after the Atwood is stopped.
But also such that when at rest the lever swings low enough to provide clearance
for the smaller weight to rise.


The chain goes from the lower lever, under a pulley and up to the short end of
the upper lever, such that when the Atwood drops, the heavy weight hits the lever,
pulling the chain, activating the other lever
Sending the smaller weight upwards, operating the Atwood in an upward vector
and measure the rise of the larger weight as the smaller weight reaches the end
of its string.

[sm0ky2]

If it can lift the larger weight all the way back up,
Then the energy produced would be


The m of the smaller weight, * 9.8 * the length of the string

[Floor]

The RATE here (in the graph attached below) at which the acceleration is occurring, is constant.
             (3 meters per second per second in the graph)

This is like when gravity accelerates an object while within a vacuum.
             (9.80665 meters per second per second when caused by Earth's gravity)

The kinetic energy in a free falling object increases within each interval of time
within which it free falls.  This is so even though the force of gravity is constant
during that free fall.

The RATE AT WHICH THE SPEED IS INCREASED is the same in each given time
interval.

The SPEED ITSELF, that the object is traveling at is greater in each successive interval
of time that passes.

There fore the object is moving faster and travels farther in each successive interval of time,
than it did during the previous interval of time.

The momentum of a given mass or object is greater when its speed is greater.

momentum = mass * velocity
momentum = force * time

The longer the time that a given force acts upon an object that it is ACCELERATING,
the faster that objects moves, the greater is that objects momentum, and the greater is
the kinetic energy of that object due to that motion.

Ek = 1/2 * mass * velocity ^2

But also I agree that actual measurements and experiments are what are probably
most appropriate to the topic so...  I'll bow out for now.

      Again
         best wishes
               floor

P.S.
   Given that the mass of the object remains constant, the reason the rate of
acceleration is constant ... is because the force applied is constant.

  The energy reqired to maintain the force as constant increases through out each
  interval of time.

[sm0ky2]

This will hold true in the vertical domain if the force applied is from gravity alone
(or more appropriately stated: at vectors perpendicular to the center of gravity of the source field)

The same if the force applied was constant in the horizontal on a rigid surface
Such that gravity could be negated.


In either case, the second derivative can be negated, as its' effective value is 0


But the full equation allows for analysis of both an applied force,
and the force of gravity, at any vector.


A 'ballistics calculator' does this for us, and can be used in automated trajectory devices.
Or in the field using manually controlled ballistics
The solid-state version of the quivering nerd in the trenches with a notepad


Gravity will always prove to be a conservative field in the perpendicular vector.
And consistent in most locations. (there are anomalies that could be exploited)
What we put in to lift a mass, will always return the same; minus wind resistance,
and other losses.

[sm0ky2]

In the most extreme example, we have a slim 1 meter rod of titanium with pointed ends.
We launch this straight up using a small railgun coil, a series of capacitors and a small power supply


It leaves the rail gun at approximately 10km/sec
And returns in roughly the same general area at about 8 km/sec


Thats mach 23, it destroys the launch-site and the rod,
leaving nothing but a crater.


Consuming 30MW for 5 seconds
Returning with a power of 0.126GJ
And a loss of ~ 15% of our power
And about 20$ from our pockets


Your railgun must be engineered to NOT exceed 10km/sec
or you risk endangering low-orbit technologies.