A Ball Through The Center of the Earth

In summary, the conversation discusses the behavior of a ball dropped through a hole drilled at the center of a spherical, solid, and uniform density Earth. The first case considers the ball dropping from one pole to the other, while the second case looks at the ball dropping from the equator. It is concluded that in order to preserve angular momentum, the ball would have to collide with the side of the hole in the second case, as the rate of rotation of the Earth and the ball would need to increase.
  • #1
joesniper100
1
0
Hello everyone,
I will begin by saying if this question is a repeat, I am sorry. I searched and only found similar questions but not any discussion on this specific point. With that that:

Consider an ideal model of Earth: uniform density, spherical, solid mass.

The classic question is if a hole is drilled through the center along the axis of rotation, and a ball is dropped, what will be it's behavior. I know this means that (neglecting air resistance) the ball will oscillate from one pole to the other with the same period as a revolution around the circumference of the earth.

Case 2: The ball is now dropped from the equator through a hole drilled through the center to the other side. Will this ball hit the side of the hole?

Please see attached image for my work. Because omega works out to be constant this should mean that the ball never hits the side.

What are your thoughts?
 

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  • #2
Angular momentum of the ball and Earth are preserved since there are no external forces. As the ball falls towards the center of the earth, in order to preserve angular momentum, the rate of rotation of Earth and ball would have to increase. This can only happen if the ball collides with the side of the hole and generates impulses or a continuous force on the side of the hole in order to increase the Earth's rate of rotation the tiny amount it takes to preserve angular momentum as the ball approaches the center of the earth.

Once past the center, as the ball falls "outwards", then the rate of rotation ball and Earth has to decrease.
 

1. How long would it take for a ball to travel through the center of the Earth?

The time it would take for a ball to travel through the center of the Earth would depend on various factors such as the density of the ball, the density of the Earth's core, and the presence of any obstacles in the Earth's interior. However, based on theoretical calculations, it would take approximately 42 minutes and 12 seconds for a ball to reach the other side of the Earth.

2. Would a ball be able to withstand the extreme pressure and temperature in the Earth's core?

The Earth's core has extreme pressure and temperature conditions, with pressures reaching up to 360 GPa and temperatures reaching up to 6,000 degrees Celsius. Most objects, including a ball, would not be able to withstand these conditions and would likely be crushed or melted.

3. Would a ball be able to maintain its shape as it travels through the Earth's interior?

As mentioned before, the extreme pressure and temperature in the Earth's core would cause most objects to deform or melt. However, if we consider a ball made of a material with a very high melting point and compressive strength, such as diamond, it would be able to maintain its shape as it travels through the Earth's interior.

4. What would be the effects of the Earth's rotation on a ball traveling through its center?

The Earth's rotation would have minimal effect on a ball traveling through its center. This is because the forces acting on the ball, such as gravity and air resistance, would be balanced out by the Earth's rotation. However, the Coriolis effect, which causes objects to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, would slightly affect the path of the ball.

5. What would happen to a ball after it reaches the other side of the Earth?

Once a ball reaches the other side of the Earth, it would experience the same effects as it did during its descent, but in reverse. It would start to slow down due to gravity and eventually come to a stop at the Earth's surface. It would then start to accelerate towards the center of the Earth again, repeating the same journey back and forth until external forces act upon it to stop its motion.

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