[Phys-L] gravity along a chord
We just did gravity in my calc-based physics class. As part of that, I did
the example of a tunnel directly through the diameter of the planet, along
the rotation axis.
I have a student who wants to do a similar problem -- gravity through a
'tube' which is along a chord of the planet (assuming the planet is a
sphere, he wants to go 2 miles deep and go point to point. He thinks the
calculation will show that gravity will assist in the motion and make it a
viable transportation alternative.
I was almost certain I had sen this done in either the Physics Teacher or
the AJP, but I can't find it after a morning of searching. Does anyone know
if this has been done already?
If not, am I right in being able to tell him to just find the CM of the
portion "below" the chord, and the CM "above" the chord, and just find the
effects due to both of them at each point along the chord?
Thank you,
Peter Schoch