How Do You Calculate the Initial Speeds of Two Electrons in a Collision?

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The problem involves calculating the initial speeds of two electrons colliding head-on, where one electron has twice the speed of the other. The closest approach is given as 4.0 x 10^-14 m, and the relevant equations include the electric potential energy and kinetic energy. The user initially calculates the velocities as 1.0 x 10^8 m/s and 5.0 x 10^7 m/s but questions the textbook's single answer of 5.3 x 10^7 m/s. Ultimately, the consensus is that the user's calculations are correct, confirming the presence of two distinct velocities. This discussion highlights the complexities of energy conservation in particle collisions.
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Homework Statement


Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial speed of each electron.


Homework Equations


Ee = kq1q2 / r
Ek = 1/2 mv2

The Attempt at a Solution


I'm really lost as to how to start this. It must have something to do with electrical and kinetic energy but other than that I am mystified as to how to solve this.
 
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My first step would be to calculate the potential of 2 electrons at the given separation (equation 1)
The total KE would then be equal to this as the next step
 
OK, so I'm getting the velocities as 1.0 * 108 m/s and 5.0 * 107 m/s. I'm pretty confident about this but the textbook only gives one answer (5.3 *7 10) m/s. There should be two velocities as an answer, so I think that must be an error. Is my answer correct?
 
Millacol88 said:

Homework Statement


Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial speed of each electron.


Homework Equations


Ee = kq1q2 / r
Ek = 1/2 mv2

The Attempt at a Solution


I'm really lost as to how to start this. It must have something to do with electrical and kinetic energy but other than that I am mystified as to how to solve this.

Millacol88 said:
OK, so I'm getting the velocities as 1.0 * 108 m/s and 5.0 * 107 m/s. I'm pretty confident about this but the textbook only gives one answer (5.3 *7 10) m/s. There should be two velocities as an answer, so I think that must be an error. Is my answer correct?

I suppose yes, your answers are correct !
 
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