Neutron Stars and unbinding energy

[Minihoudini]

Homework Statement

The Gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity. the gravitational binding energy Ug is roughly given by GM^2/R. how fast do you have to smash two neutron stars to get sufficient energy to unbind them?

Homework Equations

I honestly don't know where to start. I believe my teacher is asking for the velocity and then get the energy? also what formula should I use?

The Attempt at a Solution

im thinking we use Ug=Gm^2/R and use Ug= -GMm/r and have r= Tv/2pi

 

[Andrew Mason]

The energy needed to overcome the gravitational forces keeping the neutron star matter together would have to come from the kinetic energy of the stars before collision. When they collide, that energy would have to be converted into kinetic energy of the individual molecules. Although this is thermodynamically not possible, I think that the question assumes that this is the case.

So equate the kinetic energy of two neutron stars of mass M as they are about to collide to the total gravitational binding energy of the two stars.

The question assumes that there are no inter-atomic forces other than gravity, which is not realistic.

Incidentally, the binding energy is 3GM^2/5r. See: http://en.wikipedia.org/wiki/Gravitational_binding_energy

AM

 

[kerimek]

but im not sure

I can provide a response to this content by first clarifying the concept of gravitational binding energy. This is the amount of energy required to completely separate all the particles of an object, overcoming the gravitational force that holds them together. In the case of neutron stars, which are incredibly dense and have a strong gravitational pull, the binding energy is very high.

To calculate the velocity required to unbind two neutron stars, we can use the equation for kinetic energy, KE=1/2mv^2, where m is the combined mass of the two neutron stars. This energy needs to be equal to or greater than the gravitational binding energy of the two neutron stars, which can be calculated using the formula Ug=GM^2/R, where G is the gravitational constant, M is the combined mass of the two neutron stars, and R is the distance between them.

Therefore, to unbind two neutron stars, we need to smash them together with enough velocity to produce kinetic energy equal to or greater than their gravitational binding energy. This velocity can be calculated by equating the two equations and solving for v. However, this value would depend on the mass and distance of the two neutron stars, and would likely be extremely high.

In conclusion, the velocity required to unbind two neutron stars can be calculated using the equation for kinetic energy and equating it with the gravitational binding energy equation. However, the specific value would depend on the mass and distance of the two neutron stars.