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Originally Posted by Mississippi10
Most of the confusion comes from the fact that we're used to using "pound" as both a unit of force and unit of weight, and that we seldom stop to think about the fact that gravity isn't the same everywhere. If you take a pound weight up 1000 feet, it has 1000 foot-pounds of potential energy. If you then drop it, in the absence of air resistance, it will start to fall, and every second it will be falling 32 feet per second faster than it was a second before. In slightly less than eight seconds, it will be falling a little over 250 feet per second, and it will have fallen 1000 feet. If you plug 252 ft/sec and 1 pound into the proper formula, you'll get 1000 foot pounds, only now the potential energy it had a thousand feet up has been changed into kinetic energy by the force of gravity.
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I hate to be a stickler and I mean no disrespect, but I feel I need to clarify a few things in your post. Please don't take it the wrong way, you're not wrong per se, but I need to add a few things:
1) Weight is force with a specific vector, i.e. it has magnitude and direction, which points downward to the center of the Earth at all times. Force is a vector that may point any which way at any given time.
2) On or near Earth's surface, gravity is nominally the same. If a space shuttle wasn't in orbit, i.e. it stood still, it would still feel about 90% of Earth's gravity and start to move towards the center of the Earth at about 29ft/(s^2). Keep in mind a typical space shuttle orbit is about 250 miles above sea level.
3) Your example with the falling object is fundamentally correct. Mechanical energy is conserved at all times. In a closed system, Total Energy = Potential Energy + Kinetic Energy = mass*gravity*height + 0.5*mass*(velocity^2). A 1lbf object
at rest at 1000ft AGL will have the same energy if it was released to free fall to 0ft, because 100% of its potential energy was converted to kinetic energy. Total Energy on its way down does not change since as potential energy is getting smaller, kinetic energy is getting larger and they add up to total energy at all times (assuming no friction, etc).
Again, please don't take this as I'm saying you're wrong, because you're not, it's just that since we've opened this can of worms, I feel like things should be defined as clearly as possible.
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