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Name: Bart
Status: Educator
Age: 40s
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Question:
How is weight affected from within the mass of a large spherical body? This question came up in my daughter's 7th grade science class. She posited a thought experiment that at the exact center of the earth a person would weigh nothing, and that weight would increase as one moved toward the surface. Her teacher countered that one weighs more inside a cave than on a high mountain, seeming to contradict my daughter. Aren't they both correct? Wouldn't weight be greatest on the surface of a round sphere? Any advice/websites you could offer would be most deeply appreciated. (No pun intended!)



Replies:
Great question!

Paul Hewitt has written a good explanation of this in his book, Conceptual Physics, 3rd Edition (Addison Wesley) 1997. Read Chapters 12 and 13. In brief, the gravitational force drops off as the inverse square from the surface of the earth as we go out. But what happens as we dig into the earth? We now have mass attracting us from above, as well as from below. The gravitational force is somewhat reduced. As we go further and further into the planet, this becomes more noticeable, so that when the center of the planet is reached, you are being pulled equally on all sides (assuming uniform distribution of mass), and the net gravitational force is zero.

Therefore, the gravitational forces are greatest on the surface of the planet, and diminish when you go above or below the surface. On the mountain, we are further away, while in the cave, we have some mass above us. In both cases, the gravitational force will be less than that at the surface.

I hope this helps!

Nathan A. Unterman
Glenbrook North High School
2300 Shermer Road
Northbrook, IL 60062-6700



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