1. Sep 25, 2015

Frank Einstein

1. The problem statement, all variables and given/known data
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?

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

3. 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?

2. Sep 25, 2015

Staff: Mentor

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).

3. Sep 25, 2015

Frank Einstein

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)?

4. Sep 25, 2015

Orodruin

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

5. Sep 25, 2015

Frank Einstein

A
Allright. I gess that I will do that.

Thak you very much both of you.