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ghostops
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Question: A body of mass m is moving in a repulsive inverse cubed force given by
Work done so far:
we did a similar problem with inverse square so I am attempting to modify that for use with cubes
so far I have
Thank you in advance
F = K/r^3 where K > 0
show the path r(θ) of the body given by1/r = A cos[β(θ-θο)]
Find the values of constants A and β in terms of E, L.Work done so far:
we did a similar problem with inverse square so I am attempting to modify that for use with cubes
so far I have
F = K/r^2+K/r^3
V(r) = ∫ F(r)dr
V(r) = K/r + K/2r^2
dr/dθ = r^2/L√[2u(E-L^2/2ur^2-K/r - K/2r^2)]
distributing and moving L
dθ=dr/r^2 1/√[2uE/L^2 - 1/r^2 - uK/L^2r^2 - 2uK/L^2r]^-½
substituting 1/r for ω and dr/r^2 for dω
dθ=dω1/√[2uE/L^2 - ω^2 - uKω^2/L^2 - 2uKω/L^2]^-½
from here our professor wants us to reduce this to dθ=dω/√(a^2+x^2) so we can use trig sub we are running into issues and don't really know how to move forward. any help would be useful.V(r) = ∫ F(r)dr
V(r) = K/r + K/2r^2
dr/dθ = r^2/L√[2u(E-L^2/2ur^2-K/r - K/2r^2)]
distributing and moving L
dθ=dr/r^2 1/√[2uE/L^2 - 1/r^2 - uK/L^2r^2 - 2uK/L^2r]^-½
substituting 1/r for ω and dr/r^2 for dω
dθ=dω1/√[2uE/L^2 - ω^2 - uKω^2/L^2 - 2uKω/L^2]^-½
Thank you in advance