Exploring the Earth's Center: Ball Drop Speed vs Distance Plot

In summary, the question being discussed is what the speed versus distance plot would look like if a ball was dropped down a hole drilled through the Earth. There are additional assumptions being made, such as no wind resistance and the Earth being a sphere with uniform density and no spinning. The conversation also mentions solving for the gravitational field using Gauss's law, resulting in a mass-spring system. This type of question is commonly discussed in undergraduate mechanics courses.
  • #1
Molydood
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If I drilled a hole all the way through the earth, and then dropped a ball down one end, what do you think the speed versus distance plot would look like?

I am interested in the centre point of the Earth primarily - instinct tells me it would overshoot by quite a bit, but how far?

assume no wind resistance
 
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  • #2
Molydood said:
If I drilled a hole all the way through the earth, and then dropped a ball down one end, what do you think the speed versus distance plot would look like?

I am interested in the centre point of the Earth primarily - instinct tells me it would overshoot by quite a bit, but how far?

assume no wind resistance

And if other assumptions to be made include the Earth as a sphere with uniform density, no spinning, etc... then if you solve for the gauss's law equivalent for the gravitational field, you'll get a mass-spring system!

This is a common question in undergraduate mechanics course.

Zz
 

What is the purpose of exploring the Earth's center?

The purpose of exploring the Earth's center is to gain a better understanding of the planet's composition, structure, and processes. This can help scientists make predictions about natural phenomena and better understand the history of Earth.

What is a ball drop speed vs distance plot?

A ball drop speed vs distance plot is a graph that shows the relationship between the speed at which a ball falls and the distance it has traveled. This can be used to study the effects of gravity and air resistance on the motion of objects.

How is the data collected for a ball drop speed vs distance plot?

The data for a ball drop speed vs distance plot is typically collected by dropping a ball from a known height and recording the time it takes to reach different distances. This data is then used to calculate the ball's speed at each distance, which is plotted on the graph.

What can a ball drop speed vs distance plot tell us about the Earth's center?

A ball drop speed vs distance plot can provide information about the strength of Earth's gravity at different depths. It can also reveal the effects of air resistance and other forces on falling objects, which can give insights into the composition and density of Earth's layers.

What are the limitations of using a ball drop speed vs distance plot to explore the Earth's center?

While a ball drop speed vs distance plot can provide valuable information, it has limitations. For example, it does not account for variations in gravity due to the Earth's rotation and shape. It also only provides information about a small portion of the Earth's center, as it is not possible to directly measure deeper layers.

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