What Happens When a Pebble is Dropped Through Earth's Core?

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Discussion Overview

The discussion explores the hypothetical scenario of a pebble dropped through a tunnel bored through the Earth's core, focusing on the resulting motion of the pebble, including concepts of simple harmonic motion (SHM), air resistance, and the effects of Earth's rotation on the pebble's trajectory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that if a pebble is dropped into a tunnel through the Earth's center, it would perform simple harmonic motion (SHM) if air resistance is ignored.
  • Others argue that air resistance would significantly affect the motion, suggesting that the pebble would not exhibit true SHM initially and may eventually stop at the center due to energy loss from friction.
  • A participant mentions that assuming a vacuum and a perfectly spherical Earth, the pebble could theoretically oscillate indefinitely in SHM.
  • Another participant raises a question about the effect of Earth's rotation, suggesting that if the hole is drilled along the equatorial plane, the pebble might strike the inner wall of the hole due to the Earth's movement during the time it takes the pebble to travel through the tunnel.

Areas of Agreement / Disagreement

Participants express differing views on the effects of air resistance and the conditions under which SHM would occur. The impact of Earth's rotation on the pebble's trajectory also remains a point of contention, indicating that multiple competing views exist without a consensus.

Contextual Notes

Assumptions about the Earth's structure, the nature of the tunnel (e.g., vacuum, spherical Earth), and the effects of air resistance are critical to the discussion but remain unresolved.

nami habib
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if a tunnel is bored through the centre of the Earth and a pebble is dropped into it then the pebble will do what ?...A)stop at centre...b)perform s.h.m.
 
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SHM for a considerable period of time, given that it would have gained enough momentum to defy gravity and travel to the other end of the hole by the time it reaches the centre. And then gravity pulls it right back.[EDIT: And that's if the hole is drilled from pole to pole.]
 
vhbelvadi said:
SHM for a considerable period of time, given that it would have gained enough momentum to defy gravity and travel to the other end of the hole by the time it reaches the centre. And then gravity pulls it right back.[EDIT: And that's if the hole is drilled from pole to pole.]

But you are neglecting the considerable air resistance. So it will not be close to SHM in the beginning.

I'm of course assuming that molten rock/metal will not refill the hole when the drill is removed...
 
Assuming the tunnel was bored through a perfectly spherical Earth and was in a vacuum then it would SHM for quite a while if not indefinitely.
 
nami habib said:
if a tunnel is bored through the centre of the Earth and a pebble is dropped into it then the pebble will do what ?...A)stop at centre...b)perform s.h.m.
IF you are ignoring air resistance then you will have harmonic motion- just as vhbelvadi says. Energy will be conserved so the pebble will accelerate until it reaches the center of the earth, decelerate so that it stops just as it reaches the surface at the other end of the tunnel, then repeat its motion.

IF you are not ignoring air resistance, then Energy is not conserved. Depending upon just how much energy is lost to friction, the pebble may perform "damped" harmonic motion for several repetitions, eventually stopping at the center of the earth, as torquil says.
 
thnx guys
 
I was just wondering, if the hole drilled has a radius that is considerably small and we assumed a vacuum (so there's no question of air resistance) and the hole was drilled along the equatorial plane, would the pebble actually reach the other end at all or would it strike an inner wall of the hole because the Earth would have rotated quite a distance by that period of time?

(I reckon it would take the pebble about 19min to reach the centre so roughly double to reach the opposite end of the tunnel which means the Earth would have moved thousands of metres by then.)
 

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