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

[fondah]

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?

 

[Doc Al]

No. Think about it. If there's no acceleration at the center (which is correct), how can it stop?

 

[fondah]

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?

 

[Doc Al]

Sounds good to me.

 

[fondah]

Thanks so much

 

[DaveC426913]

...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.

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.

 

[fondah]

So could I use the simple harmonic motion equations with this oscillation?

 

[Doc Al]

So could I use the simple harmonic motion equations with this oscillation?

Sure.