The discussion centers on calculating the position where a moving proton, with an initial speed of 1.23 x 104 m/s, stops momentarily before reversing direction due to the repulsion from another fixed proton. The conservation of energy principle is applied, equating the initial kinetic energy (Ek = 0.5 * m * v2) to the electric potential energy (U = k * e2 / r). The correct formula for the distance (r) is derived as R = 2k * e2 / (m * v2), leading to a final answer of approximately 1.821 x 10-9 meters.
PREREQUISITESStudents studying physics, particularly those focusing on electromagnetism and energy conservation, as well as educators seeking to clarify concepts related to particle interactions.
Assuming that the second proton is fixed in place
Delphi51 said:The proton is moving initially so it has kinetic energy.
You must think about what energy change takes place as it is repelled by the other proton. The calculation itself will be easy.
Delphi51 said:It lost kinetic energy. But energy is conserved; it must have changed into some other kind of energy. It is the energy due to electric charges being near each other and is called electric potential energy. It depends on the distance between charges.
Write "initial kinetic energy = electric potential energy when stopped"
Put in the detailed formulas for both types of energy. Wikipedia has the potential energy one here: http://en.wikipedia.org/wiki/Electric_potential_energy
Then you can solve for the distance between charges.
Delphi51 said:Your calc looks okay but I don't get the same answer.
The elementary charge IS 1.6 x 10^-19, so you should not have got a different answer that way!
You know, it is much easier to solve the equation before putting the numbers in - just easier to manipulate letters than lengthy numbers.
k*e²/R = ½m⋅v²
R = 2k*e²/(m⋅v²)
Putting in the numbers at this stage, I get an answer in nanometers.