Special Relativity problem regarding relat. energy/ momentum

In summary, the conversation discusses an inelastic collision between two objects, one with a mass of 90 kg and traveling at a speed of 0.850c, and the other with a mass of 1400 kg. After the collision, the two objects stick together. The conversation also mentions confusion about the concept of relativistic mass and its relevance in this situation. The experts clarify that it is the rest mass of the object that changes due to an increase in energy, and suggest looking into the concept of mass-energy equivalence.
  • #1
erwinxa
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  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?
 
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  • #2
Look at the energy-momentum four-vector on page 25
http://webee.technion.ac.il/people/boaz/Downloads/AnIntermediateLevelIntroductionToSpecialRelativity.pdf
 
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  • #3
andrevdh said:
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?
 
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  • #4
erwinxa said:
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
 
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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.
 
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  • #6
Thank you
andrevdh said:
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!
 

Related to Special Relativity problem regarding relat. energy/ momentum

1. What is the concept of special relativity in relation to energy and momentum?

Special relativity is a theory in physics that explains the relationship between energy and momentum in objects moving at high speeds. It states that as an object's speed increases, its mass also increases, and its measurements of length and time are affected. This theory also shows that mass and energy are interchangeable and can be converted into each other through the famous equation E=mc^2.

2. How does special relativity affect the conservation of energy and momentum?

Special relativity does not change the laws of conservation of energy and momentum. However, it adds a new understanding of how these quantities are conserved in systems moving at high speeds. In special relativity, the total energy and momentum of a closed system remain constant, but they can be converted into different forms, such as mass and kinetic energy, as the object's speed changes.

3. Can special relativity explain the phenomenon of time dilation?

Yes, special relativity can explain time dilation, which is the concept that time appears to pass slower for objects moving at high speeds. This occurs because as an object's speed increases, its measurements of time slow down relative to a stationary observer. This effect is essential for understanding the behavior of particles moving at near-light speeds.

4. How does special relativity affect our understanding of the speed of light?

Special relativity shows that the speed of light is constant in all inertial frames of reference, regardless of the relative motion between the observer and the source of light. This means that the speed of light is the same for all observers, regardless of their speed or the direction they are moving. This concept is crucial in understanding the behavior of objects moving at high speeds.

5. What are some practical applications of special relativity in modern technology?

Special relativity has many practical applications in modern technology, including particle accelerators, GPS systems, and nuclear energy. It also plays a critical role in the development of space technology, as it helps us understand the behavior of objects in space and the effects of high speeds on their measurements of time and distance.

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