Gravitation (just to check if calculation is right) (1 Viewer)

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I was wondering if someone could tell me if I did this right:

Two neutron stars are separated by a distance of 10^10m. They each have a mass of 10^30kg and a radius of 10^5m. They are initially at rest relative to each other. How fast are they moving when they collide?

R = 2r + d = 2(10^5)+10^10

v = sqrroot (2Gm2/R^2), sub in all the numbers and v = 1.2x10^5m/s
 

HallsofIvy

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Hollysmoke said:
I was wondering if someone could tell me if I did this right:

Two neutron stars are separated by a distance of 10^10m. They each have a mass of 10^30kg and a radius of 10^5m. They are initially at rest relative to each other. How fast are they moving when they collide?

R = 2r + d = 2(10^5)+10^10

v = sqrroot (2Gm2/R^2), sub in all the numbers and v = 1.2x10^5m/s
Where did you get "v= sqrroot(2Gm2/R2"? Shouldn't that be v= sqrroot(2Gm2/R)?
 
Hmm I think I rearranged the equation wrong then. Thanks.
 
I did Fg = Gm1m2/r^2 = 1/2mv^2
 

Andrew Mason

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Hollysmoke said:
I was wondering if someone could tell me if I did this right:

Two neutron stars are separated by a distance of 10^10m. They each have a mass of 10^30kg and a radius of 10^5m. They are initially at rest relative to each other. How fast are they moving when they collide?

R = 2r + d = 2(10^5)+10^10

v = sqrroot (2Gm2/R^2), sub in all the numbers and v = 1.2x10^5m/s
The total work done is the integral of the force from initial r to final r:

[tex]\int_{r_i}^{r_f}Fdr = \int_{r_i}^{r_f}\frac{Gm^2}{r^2}dr = Gm^2\left(\frac{1}{r_i} - \frac{1}{r_f}\right)[/tex]

This becomes the kinetic energy of both stars, each of which has half this energy:

[tex]KE_{star} = \frac{1}{2}mv^2 = \frac{1}{2}Gm^2\left(\frac{1}{r_i} - \frac{1}{r_f}\right)[/tex]

[tex]v = \sqrt{Gm\left(\frac{1}{r_i} - \frac{1}{r_f}\right)}[/tex]

AM
 
We haven't done integrals in this unit so I don't know how to solve that method =(
 

Andrew Mason

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Hollysmoke said:
We haven't done integrals in this unit so I don't know how to solve that method =(
All you need to know is that the potential energy is [itex]U = -GmM/r[/itex]. The change in potential energy between two positions is just [itex]\Delta U = -GmM(1/r_f - 1/r_i)[/itex]. This is the change in potential energy of the system. In this case, the system consists of two stars which move toward each other with equal speed.

AM
 

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