How to Calculate the Initial energy of two protons colliding

[msPhysics]

Homework Statement

Tow protons of equal energy collide head on and the result is

p+p -----> p+p+ Pi⁰

If all particles produced at rest what must be the KE of the initial protons

Homework Equations

mass of Pi⁰ = 135MeV/c²

The Attempt at a Solution

Total energy of the system, E= mc²

Mass of proton = 1.6726 *10^-27 Kg

Hence initial energy = 2* 1.6726*10^-27*2.99*10⁸*2.99*10⁸

But in this case why do I need the mass of Pi 0...I guess I am terribly worng pls help

 

[vela]

The initial energy isn't just the sum of the rest energies because the protons are moving.

What about after the collision?

Hint: Use the 938 MeV/c² for the mass of the proton. It'll make the calculations simpler — no unit conversions needed.

 

[msPhysics]

The initial energy isn't just the sum of the rest energies because the protons are moving.

What about after the collision?

Hint: Use the 938 MeV/c² for the mass of the proton. It'll make the calculations simpler — no unit conversions needed.

I didnt get you...could you may be explain a bit more

 

[vela]

The total energy of a particle is equal to E=mc²+K, where K is the kinetic energy and m is the rest mass.

 

[rwisz]

The mass of the Pi0 is necessary to calculate the total energy of the system because it is one of the particles produced in the collision. The equation E=mc^2 applies to all particles, including the Pi0. In order to calculate the initial energy of the protons, we need to take into account the energy of the Pi0 as well.

To calculate the initial energy of the protons, we can use the equation E=mc^2 and plug in the mass of the proton (1.6726 * 10^-27 kg) and the speed of light (2.99 * 10^8 m/s). This will give us the total energy of one proton. Since we have two protons colliding, the initial energy would be twice this value.

However, we also need to factor in the energy of the Pi0. The mass of the Pi0 (135 MeV/c^2) can be converted to kg using the conversion factor 1 MeV/c^2 = 1.783 * 10^-30 kg. This gives us a mass of approximately 2.41 * 10^-28 kg for the Pi0.

Now, we can use the equation E=mc^2 again, but this time we will plug in the mass of the Pi0 and the speed of light to calculate its energy. This energy will be added to the initial energy of the protons.

So, the final equation would be:

Initial energy of protons = 2*(1.6726 * 10^-27 kg)*(2.99 * 10^8 m/s)^2 + (2.41 * 10^-28 kg)*(2.99 * 10^8 m/s)^2

This gives us the initial energy of the protons in Joules. To convert to MeV, we can divide by the conversion factor 1 MeV = 1.602 * 10^-13 J.

I hope this helps clarify the importance of including the mass of the Pi0 in the calculation.