What Happens to a Ball Dropped Through the Center of the Earth?

In summary, a ball of mass m dropped into a narrow hole drilled through the center of the Earth would experience no acceleration at the center, but would continue to move towards the other side due to inertia. As the acceleration increases towards the center, the ball would reverse direction and fall back down the other way. Without friction, the ball could oscillate forever in orbit around the center of the Earth, with a period of 90 minutes. The simple harmonic motion equations could be used to describe this oscillation.
  • #1
fondah
4
0

Homework Statement


You drill a narrow hole through the center of the Earth and drop a ball of mass m into it. Describe its motion qualitatively.


Homework Equations


F=-G*M*m/r^2


The Attempt at a Solution


I was thinking that the ball would fall toward the center of the Earth and then stop at the center since there would be no more acceleration due to gravity at the center of the earth. Would this be right?
 
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  • #2
No. Think about it. If there's no acceleration at the center (which is correct), how can it stop?
 
  • #3
OK, so the acceleration is 0 but the ball keeps moving toward the other side because of inertia, and as the acceleration gets stronger towards the center, it turns around and falls back down the other way. Without friction, can it oscillate forever?
 
  • #4
Sounds good to me.
 
  • #5
Thanks so much
 
  • #6
...assuming the hole is drilled through the poles. Otherwise, the rotation of the Earth will bring the ball in contact with the wall of the hole.


fondah said:
Without friction, can it oscillate forever?
Indeed, the ball is in orbit. And what's awesome is that the period of its orbit is 90 minutes, the same length of time it would be if its orbit were circular like a low-alt satellite.
 
  • #7
So could I use the simple harmonic motion equations with this oscillation?
 
  • #8
fondah said:
So could I use the simple harmonic motion equations with this oscillation?
Sure.
 

FAQ: What Happens to a Ball Dropped Through the Center of the Earth?

How does falling through the earth work?

Falling through the earth is a hypothetical scenario in which a person falls into a tunnel or hole that extends all the way through the center of the earth. As the person falls, they would experience a gradual decrease in gravitational pull until reaching the center, at which point they would be weightless. They would then begin to accelerate towards the other side of the tunnel, ultimately reaching the surface on the opposite side of the earth.

Would someone survive falling through the earth?

In theory, yes, someone could survive falling through the earth. The speed at which they would be traveling would depend on the length of the tunnel and the density of the earth's core. If the tunnel were long enough, it is possible that the person could reach terminal velocity and experience a smooth journey through the center of the earth. However, the immense heat and pressure at the core could also pose a danger to the person's survival.

What would happen to the person's body during the fall?

During the fall, the person's body would experience various changes in pressure and temperature. As they approach the center of the earth, the pressure would increase significantly, potentially causing their body to compress. However, as they pass through the center and begin traveling towards the other side, the pressure would decrease, causing the body to expand back to its original size.

Is it possible to dig a tunnel through the earth?

While it is theoretically possible to dig a tunnel through the earth, it would be an incredibly difficult and dangerous feat. The intense heat and pressure at the earth's core would make it nearly impossible for any machinery or tools to withstand, and the length of the tunnel would make it a monumental task to complete.

Would falling through the earth change the earth's rotation?

No, falling through the earth would not change the earth's rotation. The person's mass is relatively insignificant compared to the earth's overall mass, so their fall would not have a noticeable effect on the earth's rotation. The conservation of angular momentum would also prevent any major changes to the earth's rotation.

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