Exploring Algebra in Energy-Momentum-Mass Relations

In summary, the conversation is about a class discussion where the professor made a mistake in a relativistic energy momentum relation. The conversation includes equations and the discovery of the mistake by one of the students. The student apologizes for sounding stupid.
  • #1
<<Mentor note: Please always use descriptive thread titles.>>

First of all, the title is such that it attracts most views.You see, in class our professor did some goofing around numbers and variables in the relativistic energy momentum relation:
E2=(pc)2+m02c4
Since the energy required to accelerate an object to a certain velocity is
E=m0c2/√1-v2/c2,
∴E2=m02c4/1-v2/c2
plug in the value of E2,
p2c2+m02c4=m02c4/1-v2/c2
cancel out the m02c4
so p2c2=1/1-v2/c2
since c2= E/m,
⇒Ep2/m=1/1-v2/c2\
But, p2/m = 2* K.E and since E in E=mc2 implies any form of energy,and the object gains kinetic energy through it's motion, so Ek=E
⇒E(2E)=1/1-v2/c2
⇒2E2=1/1-v2/c2
⇒E2=1/2(1-v2/c2)
⇒E2=1/2-v2/c2
⇒E=1/√2-v2/c2
and that's it.No one in the room could figure out what's wrong, but our prof. said that something is wrong, but it is our job to find it out, plus, immediately one notices that if v=c, E=1 J. WTH!
 
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  • #2
This might actually be readable if you put in some parentheses.
 
  • #3
Bazinga101 said:
p2c2+m02c4=m02c4/1-v2/c2
cancel out the m02c4
so p2c2=1/1-v2/c2
That's... an interesting piece of algebra you did there.
 
  • #4
Bandersnatch said:
That's... an interesting piece of algebra you did there.
Thanks Bandersnatch, i finally find out the mistake he did, and sorry for sounding stupid
 
  • #5


This is a very interesting exploration of algebra in the energy-momentum-mass relations. It is clear that you have a strong understanding of the concepts and equations involved. However, as your professor pointed out, there is something wrong with your final result. It is important to always check your work and make sure that your equations are consistent and accurate.

One possible issue with your calculation is that you have used the equation E=mc^2, which is only valid for objects at rest. In the context of the energy-momentum-mass relations, the mass (m0) refers to the rest mass, not the total mass. When an object is in motion, its total mass increases due to its kinetic energy, so the correct equation to use would be E=√(m0c^2)^2+(pc)^2.

Another potential problem is that you have equated kinetic energy (Ek) with the total energy (E). While this may be true in some cases, it is not always the case. It is important to clearly define your variables and make sure they are consistent throughout your calculations.

Overall, exploring algebra in energy-momentum-mass relations is a fascinating topic and can lead to important insights in the field of physics. Keep questioning and exploring, and always double-check your work for accuracy.
 

What is the concept of energy-momentum-mass relations?

The concept of energy-momentum-mass relations is a fundamental concept in physics that describes the relationship between energy, momentum, and mass. It is based on Einstein's famous equation, E=mc^2, which states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared.

How does algebra play a role in understanding energy-momentum-mass relations?

Algebra is crucial in understanding energy-momentum-mass relations because it allows us to manipulate equations and solve for unknown variables. By rearranging equations and using algebraic rules, we can determine the relationships between energy, momentum, and mass in a given system.

What are some real-world applications of energy-momentum-mass relations?

Energy-momentum-mass relations have a wide range of applications in various fields, including nuclear physics, particle accelerators, and space travel. They are also essential in understanding the behavior of subatomic particles and the effects of high-speed collisions.

How does the principle of conservation of energy and momentum relate to energy-momentum-mass relations?

The principle of conservation of energy and momentum states that energy and momentum cannot be created or destroyed, only transferred or transformed. This principle is closely related to energy-momentum-mass relations because it helps us understand how energy and momentum are conserved in different physical processes, as described by Einstein's equation.

What are some common misconceptions about energy-momentum-mass relations?

One common misconception is that energy-momentum-mass relations only apply to objects moving at the speed of light. In reality, these relations apply to all objects, but the effects of Einstein's equation become more significant at higher speeds. Another misconception is that mass and energy are interchangeable, when in fact, they are two different forms of the same physical quantity.

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