B The Center of the Earth and Black holes and Gravity

[the original Bulk]

a related thought experiment to a tunnel through Earth through which a person falls to the other side, is what if it was a pendulum falling through the planet?

first, a pendulum is at 90 degs to the G field; 2nd, as soon as the pendulum BEGINS to fall through, it is in free fall, and it will continue its last swing in the same direction, at the same speed as it had when it began to fall, describing a circle. the pendulum's ACCELERATION will decrease until reaching the center of the Earth whereupon it will begin DECELLERATING until reaching the other side of the earth, all the while continuing describing the same circle. IF then, it is stopped, it will once again begin operating as a pendulum.

 

[SammyS]

a related thought experiment to a tunnel through Earth through which a person falls to the other side, is what if it was a pendulum falling through the planet?

first, a pendulum is at 90 degs to the G field; 2nd, as soon as the pendulum BEGINS to fall through, it is in free fall, and it will continue its last swing in the same direction, at the same speed as it had when it began to fall, describing a circle. the pendulum's ACCELERATION will decrease until reaching the center of the Earth whereupon it will begin DECELLERATING until reaching the other side of the earth, all the while continuing describing the same circle. IF then, it is stopped, it will once again begin operating as a pendulum.

What is ie pendulum mounted on ?

 

[the original Bulk]

It's a thought experiment. There would be other forces at work. For example, precession of the pendulum itself due to the circular motion of the end of the pendulum ( action has equal but opposite reaction.) Also, the pendulum would have to end up right-side-up at the antipode (other side of the planet), before it was grabbed, else, it would simply fall back through the earth. If the pendulum was mounted on a frame, these vectors would affect the whole apparatus accordingly.

Previous posts compared a person falling through the Earth with a pendulum at rest on the planet surface; so, I sought to toss the pendulum down the hole and derive what would happen. I wanted to keep it as simple as possible, discounting other considerations.

Noting the difference between velocity and acceleration / deceleration, is key: both man and pendulum achieve maximum VELOCITY at the center of the planet. The rate of acceleration upon beginning their downward journey is 32 ft per second per second. This rate begins to attenuate as they fall and more mass is above them until at the center the rate of ACCELERATION is zero though their velocity is greatest. Passing the center, the reverse happens, kinetic energy begins to turn back into potential until reaching the other side when motion stops, and potential is greatest again. Assuming an ideal pendulum and ignoring other forces, said pendulum would resume its normal operation.

 

[SammyS]

What object is the pendulum circling about ?

 

[the original Bulk]

Now, let's change the thought experiment, again using ideal conditions. Assume there are dual identical pendulums set in a framework that balances their combined forces such that only gravity affects them, but their swing is exactly opposite. A photo is taken at the moment they are dropped. As before, they fall through the Earth reach the other side, they are then allowed to fall back through the Earth and then return to their original positions, when another photo is taken at the exact moment of their return.

Since the only force acting upon the dual pendulums was gravity would the positions of the pendulum swings be identical in both photos?

If so, why? If not, why not?

Remember, as they are in free-fall during their journey through the Earth and back, their swings become circular motions but because they are in opposite directions, their vectors cancel each other out, leaving only the force of gravity acting upon them.

I'd say there would be no difference in their swings; the photos would be identical. It would be as if the dual pendulums had never fallen through the Earth and back.

Can anyone prove or disprove this hypothesis?

 

[the original Bulk]

What object is the pendulum circling about ?

So, the pendulum(s) only swing back forth at the surface of the earth; once dropped down the hole they are in free-fall, they no longer swing back and forth but continue in the direction of the swing at the moment they were dropped, thus making complete circles instead of back and forth motions. In the case of identical pendulums whose swings are in opposite direction with equal momentum, their angular momentum vectors cancel out.

see my post on dual pendulums.

 

[Drakkith]

Since the only force acting upon the dual pendulums was gravity would the positions of the pendulum swings be identical in both photos?

Other than because of coincidence, why would they be?

 

[the original Bulk]

Other than because of coincidence, why would they be?

Why would they not be, since they were synchronized (though in opposite directions) in Earth's 1 G field before dropping into the hole, stayed in Earth's field until they passed all the way through the planet and back, returning to their precise starting point?

 

[Drakkith]

Because they are counter rotating. I would think it would just be coincidence that they would be back at their identical positions when they return to the starting point.

 

[Evo]

a related thought experiment to a tunnel through Earth through which a person falls to the other side, is what if it was a pendulum falling through the planet?

first, a pendulum is at 90 degs to the G field; 2nd, as soon as the pendulum BEGINS to fall through, it is in free fall, and it will continue its last swing in the same direction, at the same speed as it had when it began to fall, describing a circle. the pendulum's ACCELERATION will decrease until reaching the center of the Earth whereupon it will begin DECELLERATING until reaching the other side of the earth, all the while continuing describing the same circle. IF then, it is stopped, it will once again begin operating as a pendulum.

Please post the accepted scientific sources for this. Please read our rules. We do not do thought experiments or philosophy. We deal only in accepted known science.

It's a thought experiment. There would be other forces at work. For example, precession of the pendulum itself due to the circular motion of the end of the pendulum ( action has equal but opposite reaction.) Also, the pendulum would have to end up right-side-up at the antipode (other side of the planet), before it was grabbed, else, it would simply fall back through the earth. If the pendulum was mounted on a frame, these vectors would affect the whole apparatus accordingly.

Previous posts compared a person falling through the Earth with a pendulum at rest on the planet surface; so, I sought to toss the pendulum down the hole and derive what would happen. I wanted to keep it as simple as possible, discounting other considerations.

Noting the difference between velocity and acceleration / deceleration, is key: both man and pendulum achieve maximum VELOCITY at the center of the planet. The rate of acceleration upon beginning their downward journey is 32 ft per second per second. This rate begins to attenuate as they fall and more mass is above them until at the center the rate of ACCELERATION is zero though their velocity is greatest. Passing the center, the reverse happens, kinetic energy begins to turn back into potential until reaching the other side when motion stops, and potential is greatest again. Assuming an ideal pendulum and ignoring other forces, said pendulum would resume its normal operation.

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