Question

Find the potential difference required to accelerate protons from rest to 10% of the speed of light. (at this point, relativistic effects start to become significant.)

Answer 1

To find the potential difference required to accelerate protons from rest to 10% of the speed of light, we can use the relativistic energy equation and rearrange it to solve for the potential difference. The potential difference would depend on the mass and charge of the proton, as well as the relativistic effects at that speed.

Step-by-step explanation:

To find the potential difference required to accelerate protons from rest to 10% of the speed of light, we can use the relativistic energy equation:

E = mc² / √(1 - (v²/c²))

Where E is the kinetic energy, m is the mass of the proton, c is the speed of light, and v is the velocity of the proton. We can rearrange the equation to solve for the potential difference:

V = (E + mc²) / q

Where V is the potential difference, E is the kinetic energy of the proton, m is the mass of the proton, c is the speed of light, and q is the charge of the proton. Plugging in the values, we can calculate the potential difference.

In this case, since the velocity is 10% of the speed of light, relativistic effects become significant, and we need to use the relativistic energy equation.

The potential difference required to accelerate protons to 10% of the speed of light would depend on the mass and charge of the proton, as well as the relativistic effects at that speed.

Answer 2

I don't know much about the potential difference but I certainly can calculate the energy of the proton from rest to 10% of the speed of light.

Special relativity tells us that "the energy needed to accelerate a particle (with mass) grow super-quadratically when the speed is close to c, and is ∞ when it is c."

Expressed the theory in equation is as follows:

ENERGY = rest mass × speed of light squared / (1−(“percent of speed of light”)squared ) = mc2/(1-("percent of speed of light")2)

Just plug-in the values and you can now have the answer what you are looking for!