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Originally Posted by Qfwfq
No, it definitely wasn't what I meant.
What you mean is that a rigid wall is a source of energy when you bounce a ball of it, and so is a mound of sand when it stops a ball?  |
I was expressing the conservation of momentum and energy through specific relationships; demonstrating the equivalence of 90degrees radians and whole value momentum/energy conservation.
If you have a spaceship in space and you are moving directly towards a given position, such that we consider both the ship and the position on the Z axis (coordinates x = 0, y = 0), it will require the same amount of thrust to stop the ship as it will to turn the ship 90 degrees(assuming you aim your thrust at the precise angle throughout the burn) while remaining the same vector velocity. Ie, after the turn is complete the object is still moving the same velocity.
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What you mean is that a rigid wall is a source of energy when you bounce a ball off it, and so is a mound of sand when it stops a ball?
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Momentum of a moving object can be observed to:
1) be completely transferred to another object, (think of pool ball interactions)
2) bond with an object (crash into a bucket of sand in space),
3) be observed to remain the same with the original object during a changing interaction, on a new trajectory only if it was a 90 degree change.
Interesting conclusions can be drawn from this, in a simple method.
1)If turning an object 90 degrees (without accelerating it) requires the equal expenditure of thrust (energy) that it does to stop an object, (where a moving object has a given momentum and kinetic energy, thus stopping requires an equal value) then one can easily conclude that, because 90 degrees is equal to 1/4 of a circle, than:
1/2 of a circle requires a factor of 2x...
3/4 of a circle requires a factor of 3x...
1 full circle requires a factor of 4x...(four times) the contained kinetic energy of the moving object.
or
90degrees = 1x
180degress = 2x
270degress = 3x
360degrees = 4x
What is expressed is, when given a specific vector, only 90 degree relationships will suffice as whole value transformations. If we had used a method to turn the object only 45 degrees it would only require 1/2 of the original kinetic energy and/or momentum that was originally in the system. In the case of a pool ball bouncing off a wall at 45 degrees, the wall would only supply 1/2 of the energy value measured in the pool balls total kinetic energy.
