How can two objects colliding and merging have a bigger mass?

[edoarad]

i've read that the mass of two objects which is formed when two equal objects collide must be twice the mass of the moving objects, which is grater then the sum of their rest mass. does it really happen in terms of particles? how is it explained?

thanks,
edo

 

[ghc]

I think that the mass of the final object depends on the relative speed of the two objects before colliding, if both have the same rest mass.

 

[krishna mohan]

That is right...the extra kinetic energy must have gone somewhere...we might say that it is converted to heat or some other form of internal energy..but since energy equals mass, this extra energy will give a greater mass to the final system..thus it is also true that you can make a body more massive by just raising its temperature...Please refer the book on special relativity by Resnick...section 3.6..

 

[edoarad]

thank you very much.
does a body whose mass has been increased by high temprature acts the same as though he was simply that massive? how hot must something be in order for the added mass not to be neglectable?

 

[HallsofIvy]

Heat isn't the only kind of energy. [math]E= mc^2[/math] so [math]m= E/c^2[/math]. How large that has to be to be "not neglectable" depends upon what you consider "negletable".

 

[edoarad]

i thought that the energy from e=mc^2 is simply the energy that can be gained by using the mass, is that wrong?

 

[diazona]

Well, it depends on what you mean by "using". E = mc^2 is the amount of energy you'd get if you completely converted the mass into energy. For instance, by reacting matter and antimatter. If that's what you mean by "using", then sure, E = mc^2 is the amount of energy you can get. But a normal definition of "using" probably entails something like nuclear fusion, or burning - some process in which there's still some mass left at the end - and in that case you only get a small fraction of mc^2 as useful energy.

 

[HallsofIvy]

i thought that the energy from e=mc^2 is simply the energy that can be gained by using the mass, is that wrong?

It works both ways: mass contains energy, energy has mass.

 

[edoarad]

i think I've got it now, thank you.

 

[krishna mohan]

And if you want to do a small calculation to see how temperature can affect mass, just equate mc^2 and kT, where k is the Boltzmann constant and T is the temperature,,,,and calculate T for some amount of mass..