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

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Homework Help Overview

The problem involves a ball dropped through a hole drilled to the center of the Earth, exploring its motion and the effects of gravity and inertia during the fall.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the ball's motion towards the center of the Earth, questioning how it can stop if there is no acceleration at the center. They explore the concept of inertia and whether the ball can oscillate indefinitely without friction.

Discussion Status

Some participants have offered insights into the nature of the ball's motion, suggesting it may oscillate due to inertia. There is an acknowledgment of the conditions under which this motion occurs, such as the assumption of no friction and the orientation of the hole.

Contextual Notes

Participants note the importance of the hole's orientation and the impact of Earth's rotation on the ball's motion, raising questions about the conditions necessary for the described behavior.

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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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No. Think about it. If there's no acceleration at the center (which is correct), how can it stop?
 
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?
 
Sounds good to me.
 
Thanks so much
 
...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.
 
So could I use the simple harmonic motion equations with this oscillation?
 
fondah said:
So could I use the simple harmonic motion equations with this oscillation?
Sure.
 

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