What is the accelaration between two protons when they are touching?

Question

When we are sitting with our bottom on the earth's surface are we moving towards the eath's center or are we standing still?

acceleration comparison applies same wayto particle as protons?

Answer 1

Zero when they are touching. Sounds weird? Yes, indeed there is a force between the protons due to the Coulumbic repulsion. But when they are touching, they are not moving, unless they are free to move away from each other, no longer touching each other. Then, the electrostatic force=e²/4πεr²=ma, hence the acceleration,

a=e²/4πεmr², where e is the electronic charge, π=3.142, ε is the permitivity in free space, m is mass of the proton, r is the radius of the proton. I do not have these values, but it is worth knowing the formula.

Answer 2

On the surface, this question might look like a simple electrostatic question....two like charges placed very close together will repel with a force described using Coulombs law,

F = k * (Q * q) / r^2
where F is the force, k is the electrostatic constant, Q and q are the charges on the two particles, and r is the radial distance between the charged.

However,
the Protons in question are VERY close together, so close in fact that that are "touching".

In the nucleus of an atom, there are many protons (and neutrons) all stuck together...why are these particles not flying apart?
Well it is because there is another force, much stronger than the electrostatic force which holds attracts them rather than repelling them, this is called the Strong Nuclear Force.

The Strong Nuclear force gets very weak with distance, this is why it has no significant effect at all outside the nuclei of atoms (on the order of E-15 meters).
But if one can get a proton so close to another proton that they actually touch, the Strong Nuclear Force would be significant, far more significant than the electromagnetic forces or gravity.