The discussion revolves around calculating the center of mass for a cone, with specific focus on the implications of using surface density versus volume density in the context of a hollow versus solid cone. Participants are exploring the integration methods necessary for this calculation.
The discussion is active, with participants providing feedback and asking for further details, such as the actual problem statement and calculations. There is a mix of interpretations regarding the density to be used, and some guidance has been offered on setting up integrals for both solid and hollow cones.
There is a noted ambiguity regarding whether the cone is solid or hollow, which affects the choice of density and integration method. Participants are also responding to the absence of the original problem statement, which may limit the clarity of the discussion.
In part a, the cone is a solid, not hollow, so you want to use the volume density ρ=m/V, where m is the mass of the cone and V is its volume.eileen6a said:a) i use surface density and calculate the mass of a disk and integrate it from bottom to top. Is it right? But the cone is hollow so i only need to use the mass of the circuference?
For part c, it's not quite a simplification. This time you do want to use the surface density σ=m/A, where A is the surface area of the cone, and setting up the integral is a bit different.b) use "negative mass"? are there any other approaches?
c) is it just a simplification of part a)?
thx!