Gravitation (just to check if calculation is right)

In summary: The total work done is the integral of the force from initial r to final r:\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)This becomes the kinetic energy of both stars, each of which has half this energy:KE_{star} = \frac{1}{2}mv^2 = \frac{1}{2}Gm^2\left(\frac{1}{r_i} - \frac{
  • #1
Hollysmoke
185
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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
 
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  • #2
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)?
 
  • #3
Hmm I think I rearranged the equation wrong then. Thanks.
 
  • #4
I did Fg = Gm1m2/r^2 = 1/2mv^2
 
  • #5
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
 
  • #6
We haven't done integrals in this unit so I don't know how to solve that method =(
 
  • #7
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
 

1. How is the gravitational force between two objects calculated?

The gravitational force between two objects can be calculated using the formula F = G(m1m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

2. What is the value of the gravitational constant?

The value of the gravitational constant is approximately 6.67 x 10^-11 Nm^2/kg^2.

3. How does the distance between two objects affect the gravitational force between them?

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases.

4. What is the difference between mass and weight in relation to gravitation?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, but weight can vary depending on the strength of the gravitational force.

5. How does the mass of an object affect the strength of its gravitational pull?

The greater the mass of an object, the stronger its gravitational pull will be. This is because a larger mass means a greater amount of matter, which results in a stronger gravitational force.

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