Express the potential energy U in terms of M and v

[leonne]

Homework Statement

For a finite isothermal sphere with a radius R and circular velocity v (remember,
the rotation curve is constant), we derived the total mass and potential energy as
M =v²R/G

U = -GM²/R
Express the potential energy U in terms of M and v. Use the virial theorem to
find the kinetic energy K and total energy E (again in terms of M and v).

Homework Equations

The Attempt at a Solution

Kind of confused about the first part to find potential in terms of m and v.
Would I just sub total mass equation into potential? I get U=-v⁴R/G
Is this right? Hmm seems like what i did is wrong. Is it saying that the potential energy can only have M and V?

 

[Mindscrape]

It said m and v so I would think you would want to have
U=-v^2 M

 

[leonne]

O yea seems that would work you would get the same units when u get the answer thxs

 

[leonne]

For this part
Use the virial theorem to
find the kinetic energy K and total energy E (again in terms of M and v).
Would the answers be k=-v^2M/2 E=v^2m/2
I think the virial theorem is E=-(K)=(U/2)