Astrophysics
  • Astrophysics
@empty
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Astrophysics
  • Astrophysics
I made a post cause I had odd number questions asked and that looked gross
Empty
  • Empty
cool let's check it out
Astrophysics
  • Astrophysics
Now find the force law for a central force field that allows a particle to move in a logarithmic spiral orbit given by \[r = k e^{\alpha \theta}\], where k and alpha are constants

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Astrophysics
  • Astrophysics
I guess I should give you some things that will help you lol, \[\frac{ d^2 }{ d \theta ^2 } \left( \frac{ 1 }{ r } \right)+\frac{ 1 }{ r } = -\frac{ \mu r^2 }{ l^2 }F(r)\] it's pretty easy actually
Empty
  • Empty
lol what is all of this I've never seen this before
Astrophysics
  • Astrophysics
O
anonymous
  • anonymous
This is a university physics I assume?
anonymous
  • anonymous
Fansy stuff hitting the fan
Astrophysics
  • Astrophysics
This has to do with central force motion, I just assume you know everything
anonymous
  • anonymous
empty like my soul
anonymous
  • anonymous
I know the centripetal acceleration but never heard of central force
Astrophysics
  • Astrophysics
Err this will take some time to explain
anonymous
  • anonymous
I say we shoot each other with physics knowledge
anonymous
  • anonymous
I am although a classical physicist
Empty
  • Empty
I could probably figure this out but I feel like there's some method of doing this or reason for doing this.
anonymous
  • anonymous
There is reason for everything
anonymous
  • anonymous
Especially physics is a process of becoming a god
Empty
  • Empty
Haha cool so what about chemistry?
anonymous
  • anonymous
Chemistry is more earthy application based study
anonymous
  • anonymous
there is nothing theoretical about it whereas physics most are
Empty
  • Empty
Oh what do you know about chemistry?
anonymous
  • anonymous
empirical vs theoretical
anonymous
  • anonymous
Chemistry is all knowable
Empty
  • Empty
What does that mean?
anonymous
  • anonymous
Everything is empirical in chemistry
anonymous
  • anonymous
Physics mostly rely on the unreasonable effectiveness of mathematics at explaining the physical phenomena.
anonymous
  • anonymous
anyway let's get down to the central force business
Empty
  • Empty
Hahaha "Everything is empirical in chemistry"
Empty
  • Empty
I'll be damned if there aren't 8 things listed here: https://en.wikipedia.org/wiki/Theoretical_chemistry#Branches_of_theoretical_chemistry
anonymous
  • anonymous
central force depends on the distance between spherically symmetric object and the object being pondered
Astrophysics
  • Astrophysics
It has to do with the motion of a system consisted of two bodies affected by a force that is directed along the line connecting the centres of the two bodies, this is the central force. |dw:1438444424125:dw|
Astrophysics
  • Astrophysics
This sort of requires you to understand lagrangian
Astrophysics
  • Astrophysics
actually no
anonymous
  • anonymous
According to the theory everything with a mass has central force to it however minuscule they are
anonymous
  • anonymous
that equation digs up my nostalgia on universal gravitation
Astrophysics
  • Astrophysics
Actually, since I'm too lazy to derive it as it takes too long xD, just read this, if you want...http://www.astro.uwo.ca/~houde/courses/PDF%20files/physics350/Central_force.pdf
Empty
  • Empty
I can derive the euler-lagrange equation with calculus but that's just math and I get that the action gets minimized L=T-U pretty clearly. I guess the question is how do you find the kinetic and potential energy of this system in the first place?
Astrophysics
  • Astrophysics
Yeah, pretty much
Astrophysics
  • Astrophysics
Quit giving each other medals
Empty
  • Empty
lolwhat
Astrophysics
  • Astrophysics
lol
nincompoop
  • nincompoop
try to draw a path of the log central force
nincompoop
  • nincompoop
I can't see the log playing out, just yet
Astrophysics
  • Astrophysics
\[\frac{ d }{ d \theta } \left( \frac{ 1 }{ r } \right) = \frac{ d }{ d \theta } \left( \frac{ e^{- \alpha \theta} }{ k } \right) = \frac{ - \alpha e^{-\alpha \theta} }{ k }\] \[\frac{ d^2 }{ d \theta^2 } \left( \frac{ 1 }{ r } \right) = \frac{ \alpha^2 }{ r }\] \[F(r) = \frac{ -l^2 }{ \mu r^2 }\left( \frac{ \alpha ^2 }{ r } +\frac{ 1 }{ r }\right) = \frac{ - l^2 }{ \mu r^3 }(\alpha ^2+1)\]
nincompoop
  • nincompoop
true
Astrophysics
  • Astrophysics
The force law is attractive inverse cube
nincompoop
  • nincompoop
isn't it r^2 tho?
Astrophysics
  • Astrophysics
If you want to do something for fun find r(t) and theta (t)
Astrophysics
  • Astrophysics
Nope
Astrophysics
  • Astrophysics
Originally \[\frac{ d^2 }{ d \theta ^2 } \left( \frac{ 1 }{ r } \right)+\frac{ 1 }{ r } = -\frac{ \mu r^2 }{ l^2 }F(r)\]
nincompoop
  • nincompoop
looks mathematically legit
nincompoop
  • nincompoop
I am a little hurt when you said chemistry is more earthly-based :(
Astrophysics
  • Astrophysics
How is chemistry earthly based
Astrophysics
  • Astrophysics
It all started from helium and hydrogen being composed in stars, don't get me started please...
nincompoop
  • nincompoop
oh that was another dude hahaha nvm
Astrophysics
  • Astrophysics
xD
nincompoop
  • nincompoop
FOUND IT http://www.dartmouth.edu/~phys44/lectures/Chap_4.pdf

Looking for something else?

Not the answer you are looking for? Search for more explanations.