dig
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MegaFighter_X
- Post Master General
- Posts: 2334
- Joined: 27 Apr 2003 16:52
- Location: Las Vegas
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force is a vector.
From what I'm seeing here, it woudl go something like this:
ASSUME:
- tunnel dug straight though center of the earth.
- Such tunnel is structucturally sound
- such tunnel is frictionless
- Air resistance is negligible, as is any other forms of drag (making frictionless fall)
- You don't die because of pressures, etc.
- No energy gained/lost to heat
- earth's diameter is uniformly 2R = 2*radius of earth
- No earth rotation, etc.
- Closed system
THEN:
you jump, dive, or whatever into this tunnel. At the height of your jump, you have the maximum gravitational potentional enery. Like... [Accel. of Gravity*(radius of earth + height jumped)] or something like that. So you're falling. this GPE is turning into mechanical energy (if I recall from the lectures right.)
NOW:
because of teh closed system, you have the conservation of energy. When you are at the center of the earth, you have a displacement from the center of the earth of 0. G*0 = 0. Since the energy has been conserved, all the GPE turned into mechanical energy. As you rise past the center of the earth (now on the other side of the center) you start losing velocity as the mechanical energy turns back into GPE. Finally, you come out of the other side with the same height you jumped in at because of total conservation of energy. Repeat until you can get your sorry ass out of there because you didn't plan this part.
If you decide to thown in air resistance and such, then you'll end up some odd distance away from where you first started. At which point you just use hooke's law because you're basically in a spring... And you still gotta wait for someone to get your sorry ass out, because you forgot about this part...
toss out each "little" assumption, and the situation becomes more bleek...
From what I'm seeing here, it woudl go something like this:
ASSUME:
- tunnel dug straight though center of the earth.
- Such tunnel is structucturally sound
- such tunnel is frictionless
- Air resistance is negligible, as is any other forms of drag (making frictionless fall)
- You don't die because of pressures, etc.
- No energy gained/lost to heat
- earth's diameter is uniformly 2R = 2*radius of earth
- No earth rotation, etc.
- Closed system
THEN:
you jump, dive, or whatever into this tunnel. At the height of your jump, you have the maximum gravitational potentional enery. Like... [Accel. of Gravity*(radius of earth + height jumped)] or something like that. So you're falling. this GPE is turning into mechanical energy (if I recall from the lectures right.)
NOW:
because of teh closed system, you have the conservation of energy. When you are at the center of the earth, you have a displacement from the center of the earth of 0. G*0 = 0. Since the energy has been conserved, all the GPE turned into mechanical energy. As you rise past the center of the earth (now on the other side of the center) you start losing velocity as the mechanical energy turns back into GPE. Finally, you come out of the other side with the same height you jumped in at because of total conservation of energy. Repeat until you can get your sorry ass out of there because you didn't plan this part.
If you decide to thown in air resistance and such, then you'll end up some odd distance away from where you first started. At which point you just use hooke's law because you're basically in a spring... And you still gotta wait for someone to get your sorry ass out, because you forgot about this part...
toss out each "little" assumption, and the situation becomes more bleek...
John D