Relativistic Energy Calculations

[Frank Einstein]

Homework Statement

Hi everybody. I was tasked with the following exercice: Two identical protons of energy 7TeV collide head on.
Which is the total energy of the system?
How is compared this energy with the one of an Airbus 320 which mass is t50*10^6Kg at a speed of 600Km/h?
How many photons do we need for the total energy was equivalent to the Airbus?

Homework Equations

I am considering that the speed of light is 1 and it has no units.
Relativistic energy: E=Sqrt(m^2+p^2)

The Attempt at a Solution

To the first question: If both photons have the same energy, the total energy of the system must be 14 TeV; exactly twice the energy of the photon.

To the second question: Here, I write the aeroplane's energy as E=Sqrt(m^2+(m*v)^2), qhere v is the speed (all in the SI). So E=Sqrt((50*10^4)^2+((50*10^4)*(166.67))^2) =8.3*10^7J.
On the other hand 1J=1/(1.602*10^19)eV; so E =5.2*10^25eV=5.2*10^11Tev.

To the third question: 5.2/7=0.74; so we need 7.4*10^10 protons to obtain the same energy.


Can someone please tell me if I have calculated the energy of the aeroplane properly?

Thanks for reading.

 

[mfb]

You mix protons and photons, I guess you always mean protons.

To the first question: If both photons have the same energy, the total energy of the system must be 14 TeV; exactly twice the energy of the photon.

Correct.

Your Airbus mass changed from 50*10⁶ to 50*10⁴ kg? Both numbers are unrealistic, the mass should be somewhere in the range of 5*10⁴ to 10*10⁴ kg.

E=Sqrt(m^2+(m*v)^2)

This equation does not work if you use SI units. In the SI, the speed of light is not one.

Here, I write the aeroplane's energy as E=Sqrt(m^2+(m*v)^2)

That would be the total mass-energy of the airbus, but the question asks for the kinetic energy only (not explicitely, but the question wouldn't make sense otherwise).

 

[Frank Einstein]

You mix protons and photons, I guess you always mean protons.
Correct.

Your Airbus mass changed from 50*10⁶ to 50*10⁴ kg? Both numbers are unrealistic, the mass should be somewhere in the range of 5*10⁴ to 10*10⁴ kg.
This equation does not work if you use SI units. In the SI, the speed of light is not one.
That would be the total mass-energy of the airbus, but the question asks for the kinetic energy only (not explicitely, but the question wouldn't make sense otherwise).

Yeah, the mass of the Airbus is 5*10^4kg; it was a mistake.
Then, for the second question should I have written energy as the non relativistic 0.5*m*(v^2)?

 

[Orodruin]

Then, for the second question should I have written energy as the non relativistic 0.5*m*(v^2)?

Yes, this is a good approximation as 600 km/h is much much smaller than c.

 

[Frank Einstein]

A

Yes, this is a good approximation as 600 km/h is much much smaller than c.

Allright. I gess that I will do that.

Thak you very much both of you.