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I just solved an exercise in the special relativity book of A.P. French. I would like you to tell me if the answer is correct. Yes I suposse is a very easy exersice.

I hope you can help me, because I really like learn relativity and cosmology, but I have not had teachers of this, and I am completely self-taught in the subject.

In a certain reference system it is observed that a particle has a total energy of 5GeV, and an

a) What is the energy of this particle in a system where

b) What will be your mass at rest in uma?

c) What is the relative speed of the two reference systems?

Question a)

Ok, there are two systems of reference

System 1: E_1, P_1

System 2: E_2 (unknow), P_2

I apply the relativistic invariant for the four moment energy ; ##E_0^2=E^2-c^2p^2##, then: $$E_1^2-c^2p_1^2=E_2^2-c^2p_2^2$$

I make sustitution of terms: E_1=5GeV; P_1=3GeV/c; E_2=?; P_2=4GeV/c$$5^2-c^2(\frac 3 c)^2=E_2^2-c^2(\frac 4 c)^2$$ I solve and the result is: ##E_2=4\sqrt2 \text { GeV}##

Question b)

I use the reference system 2 for compute te invariant energy-momentum $$E_0^2=E_2^2 - c^2p^2$$ I put the values into the above equation: $$E_0^2=(4\sqrt 2)^2-c^2(\frac 4 c)^2$$ Solution is ##E_0=4\text{GeV}##

We can use the conversión factors and achieve a rest mass ##m_0=4.28\text{u}##, (atomic units of mass)

Question c)

For easyest calculations I use masses in GeV in this question.

In the system 2 particle have a rest mass m_0 of 4GeV, but

In ths system 1 particle have a mass of 5GeV. Then $$\frac{ m_1} {m_0}=\gamma$$$$\frac{ 5} {4}=\gamma=1.25$$

Then ##\gamma=\frac{1}{\sqrt{1-\beta^2}}##.

##\beta=0.6##, and then ##v=0.6c##

******************************************************************************************************************

Ok indications are welcome, thanks a lot.

I hope you can help me, because I really like learn relativity and cosmology, but I have not had teachers of this, and I am completely self-taught in the subject.

Exercise.Exercise.

In a certain reference system it is observed that a particle has a total energy of 5GeV, and an

*P*of 3GeV/c, (that is to say c*P*, which has units of energy, is 3GeV).a) What is the energy of this particle in a system where

*P*is 4GeV/c ?b) What will be your mass at rest in uma?

c) What is the relative speed of the two reference systems?

**My atempt of solution.**Question a)

Ok, there are two systems of reference

System 1: E_1, P_1

System 2: E_2 (unknow), P_2

I apply the relativistic invariant for the four moment energy ; ##E_0^2=E^2-c^2p^2##, then: $$E_1^2-c^2p_1^2=E_2^2-c^2p_2^2$$

I make sustitution of terms: E_1=5GeV; P_1=3GeV/c; E_2=?; P_2=4GeV/c$$5^2-c^2(\frac 3 c)^2=E_2^2-c^2(\frac 4 c)^2$$ I solve and the result is: ##E_2=4\sqrt2 \text { GeV}##

Question b)

I use the reference system 2 for compute te invariant energy-momentum $$E_0^2=E_2^2 - c^2p^2$$ I put the values into the above equation: $$E_0^2=(4\sqrt 2)^2-c^2(\frac 4 c)^2$$ Solution is ##E_0=4\text{GeV}##

We can use the conversión factors and achieve a rest mass ##m_0=4.28\text{u}##, (atomic units of mass)

Question c)

For easyest calculations I use masses in GeV in this question.

In the system 2 particle have a rest mass m_0 of 4GeV, but

In ths system 1 particle have a mass of 5GeV. Then $$\frac{ m_1} {m_0}=\gamma$$$$\frac{ 5} {4}=\gamma=1.25$$

Then ##\gamma=\frac{1}{\sqrt{1-\beta^2}}##.

##\beta=0.6##, and then ##v=0.6c##

******************************************************************************************************************

Ok indications are welcome, thanks a lot.