Dropping a mass in a hole through the Center of Earth

AI Thread Summary
The discussion revolves around calculating the weight of a 50 kg mass dropped into a hypothetical hole drilled straight to the Earth's center, assuming uniform density. Participants clarify that the gravitational force at the bottom of the hole can be determined using the formula F=GMm/r², where G is the gravitational constant, M is the Earth's mass, and r is the distance from the center of the Earth. It is emphasized that the depth of the hole, 40,230 ft, should be subtracted from the Earth's radius when calculating the effective radius for the gravitational force. The conversation highlights the importance of correctly applying the two-shell theorem in this context. Overall, the focus is on understanding gravitational force calculations in a simplified model of Earth's structure.
Pruddy
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Homework Statement


Assume that the Earth is a uniform density spherical mass. (This assumption is not correct but we will use it for simplicity in working the problem.) The deepest hole drilled into the Earth's surface went to a depth of 40,230 ft (Wikipedia.org). Imagine that this hole was straight toward the center of the Earth and that a small 50 kg spherical mass was dropped into the hole and ended up at the very bottom of it. What would be the weight of the spherical mass at that location?


Homework Equations



w=mg


The Attempt at a Solution


This is a two shell theorem problem. Since we all know that w=mg, F=GMm/r2. I think we have to find the gravitational force of the object that is at bottom of the Earth and then multiply it by its mass. This will give us the weight of the object.
 
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Welcome to PF!

Hi Pruddy! Welcome to PF! :smile:
Pruddy said:
I think we have to find the gravitational force of the object that is at bottom of the Earth and then multiply it by its mass. This will give us the weight of the object.

Yes, that's correct. :smile:

What is worrying you about that? :confused:​

(btw, don't worry about the duplicated posts, that sometimes happens :wink:)
 
Thanks for your quick reply. I do not know the right equation to use to get the gravitational force of of the mass at the bottom of the earth:confused:.
 
it's the formula you've already given … F=GMm/r2

(and of course GM/R2 = g where R is the radius of the Earth)

(btw, you mean the bottom of the hole, not the bottom of the Earth :wink:)
 
Thanks again for your quick reply. Yeah you are right, I meant the bottom of the hole. But what happends to the depth of the hole which is 40,230ft. Is it irrelevant to the question? and if it is not, will is be right to add it to the radius of the Earth before squaring it(radius)...
 
Pruddy said:
… will is be right to add it to the radius of the Earth before squaring it(radius)...

uhh? :confused:

it's a hole …

subtract it! :smile:​
 
Thanks Tim, That was very helpful...
 

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