Special Relativity problem regarding relat. energy/ momentum

[erwinxa]

1. An object having mass of 90 kg and traveling at a speed of 0.850c collides with a stationary object having mass 1400 kg. The two objects stick together. (8pts)
   1. a) Find the speed of the composite object.
   2. b) Find the mass of the composite object
      

Hello, I would appreciate any insight into the above problem, I have the solution, yet I do not understand their approach which ultimately finds the relativistic momentum and divides the relativistic Energy equations. Prior, to looking at the solution, I know this to be an inelastic collision, so I only applied the momentum equation which was incorrect. What is troubling me, is why this approach and also why I cannot consider the "final" Mass to be the 900 + 1400 if I am only considering delta P.
Thank you.

EDIT: So I've read in another textbook, why M is simply not the sum, yay, and then follows why I should consider both equations.

So I guess, my question now, simply is: since M is not the sum I should consider both. Is this correct?

 

[andrevdh]

Look at the energy-momentum four-vector on page 25
http://webee.technion.ac.il/people/boaz/Downloads/AnIntermediateLevelIntroductionToSpecialRelativity.pdf

 

[erwinxa]

Look at the energy-momentum four-vector on page 25
http://webee.technion.ac.il/people/boaz/Downloads/AnIntermediateLevelIntroductionToSpecialRelativity.pdf

thank you, I have read the section you recommended, but I thought the concept of relativistic mass was "dated", at least according to my text. my text states that mass is "now" considered an invariant. Have I misread, and am I misunderstanding the point?

 

[Chestermiller]

thank you, I have read the section you recommended, but I thought the concept of relativistic mass was "dated", at least according to my text. my text states that mass is "now" considered an invariant. Have I misread, and am I misunderstanding the point?

Yes. What you are missing is that it is the actual rest mass of the object that changes (not its relativistic mass) because the object now contains more energy. This is an E = mc² effect.

Chet

 

[andrevdh]

Early on when physicist studied nuclear processes they found that mass was "not conserved", that is the byproducts of fission
contained more mass than the original parts! Einstein made sense out of this confusing situation with his mass-energy equivalence
concept. He suggested that we should think of mass as a form of energy (which is conserved) which could change (the mass) if the energy of the object
was altered. So we found that when nucleons are removed from a nucleus work has to be done. You could think of it as the object
have been down in a well and now it has been lifted up out of it . This additional work being done increased the object's energy which
shows up as an increase in the mass of the nucleon. Google the mass energy equivalence.

 

[erwinxa]

Thank you

Early on when physicist studied nuclear processes they found that mass was "not conserved", that is the byproducts of fission
contained more mass than the original parts! Einstein made sense out of this confusing situation with his mass-energy equivalence
concept. He suggested that we should think of mass as a form of energy (which is conserved) which could change (the mass) if the energy of the object
was altered. So we found that when nucleons are removed from a nucleus work has to be done. You could think of it as the object
have been down in a well and now it has been lifted up out of it . This additional work being done increased the object's energy which
shows up as an increase in the mass of the nucleon. Google the mass energy equivalence.

Thank you. Much appreciated!