Graviational potential of 2 cones

  • Thread starter khemist
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  • #1
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Homework Statement



Consider two hollow fixed cones (such as ice cream cones without the ice cream). They have a base radius R, slant height L,and a surface mass density σ. The cones are vertical, with their apexs touching (say, at the origin). A particle initially at rest falls in from infinity, along a perpendicular bisector line. What is its speed when it reaches the tip of the cones?

Homework Equations



F = GMm/r^2
V= GMm/r

The Attempt at a Solution



So I am trying to write an equation for the cone, where if I pick any arbitrary height on the cone, I would get the circumference at that point. I would then integrate over the height of the cone. However, I am having trouble coming up with such an equations. I know that the forces in the z and y direction will cancel, so the particle will be "pulled" towards the vertex of both cones.

Would it be possible to consider the cones as a point at their center of mass?
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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Hi khemist! :smile:

I don't really understand what your cones have to do with it... :confused:

At infinity a particle of mass m and speed zero would have energy zero (arbitrary choice).
At distance 6000 km from earth (which is the radius of the earth), you can calculate the energy E=-GMm/6000km.
This will equal the increase in kinetic energy (1/2)mv^2, from which you can calculate the speed v...

Btw, note that the potential is V=-GM/r.
 

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