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Weight and Mass Affects
Name: Bart
Status: Educator
Age: 40s
Location: N/A
Country: N/A
Date: N/A
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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Update: June 2012
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