An Enclosed Mass Profile problem

  • Thread starter Thread starter bluejazz
  • Start date Start date
  • Tags Tags
    Mass
AI Thread Summary
The discussion centers on deriving the enclosed mass profile M(r) for a star based on its density function. The density is defined as rho(r) = (rho_c)[1-(r/R*)^2], where rho_c is the central density and R* is the star's radius. The user successfully integrated the density to obtain M(r) = 4(pi)(rho_c)[r^3/3 - r^5/(5R*^2)]. However, they expressed uncertainty about relating this result to the total mass M* of the star and sought clarification on the definition of central density. Ultimately, the user resolved their question independently.
bluejazz
Messages
6
Reaction score
0

Homework Statement



Find the enclosed mass profile M(r) in terms of R* and the total mass M* of the star.

Homework Equations



dMr/dr = 4(pi)r2(density)

density is given as: rho(r) = (rho_c)[1-(r/R*)2]
Where rho_c is the central density and R* is the radius of the star.

3. Attempt at a solution

I plugged the given density into the enclosed mass formula, took the integral in terms of r, and ended up with the result:

M(r) = 4(pi)(rho_c)[r3/3 - r5/(5R*2)]

My problem is, I'm not sure how to put this in terms of Mstar. What I think is I have to take the central density and the expression for volume [4/3 * (pi) * r3] and get Mstar. I guess my real question is this: what is the definition of central density?
 
Physics news on Phys.org
bump! Hope this question doesn't get lost!
 
Nevermind, I found the answer! Thanks anyways guys!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Calculating a star's density profile
Replies
3
Views
2K
Confusion on product rule for mass of differential volume element
Replies
4
Views
2K
Inverse square law of gravitation and force between two spheres
Replies
8
Views
2K
What helium mass in a balloon to make it bouyant in air?
Replies
12
Views
1K
What is density of dark matter as a function of distance from the galactic core?
Replies
1
Views
887
Coulomb's law to find electric field for charge density function
Replies
11
Views
1K
Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg
Replies
2
Views
2K
Finding an expression for the total mass of a star
Replies
1
Views
1K
Physics puzzle about the concentration of fog droplets in the air
Replies
26
Views
2K
Gravitational Forces between two masses
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top