Finding speed of two electrons initially at rest

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Homework Help Overview

The problem involves two electrons that start at rest with a specified separation and subsequently accelerate away from each other. The goal is to determine their speed when they are a significant distance apart, focusing on concepts of electric potential energy and kinetic energy.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of energy principles, questioning whether both electrons acquire kinetic energy and if their speeds can be assumed to be equal. There is an exploration of the initial calculations and the assumptions made regarding energy distribution.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made in the calculations and the treatment of kinetic energy. Some guidance has been offered regarding the need to consider both electrons' kinetic energy in the context of their motion.

Contextual Notes

There is a mention of the initial conditions, specifically that the electrons start at rest and the distance between them is defined. The discussion also hints at the need for clarity on the treatment of energy conservation in the system.

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Homework Statement


Two electrons start at rest with a separation of 5.0 x 10^-12 m. Once released, the electrons accelerate away from each other. Calculate the speed of each electron when they are a very large distance apart (Ee = 0).

Homework Equations


EE = kQq/r
Ek = (1/2)mv2

The Attempt at a Solution


EE2 - EE1 = - (Ek2 - Ek1)
- EE1 = - Ek2

(kq2) / r = (1/2)mv2
v = sqrt[ 2(8.99 x 109)(-1.6 x 10-19)2 / (9.11 x 10-31)(5.0 x 10-12) ]
v ≅ 1.0 x 107 m/s

The answer is apparently 7.1 x 106 m/s
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Hello, and welcome to PF!

Do both electrons end up with some kinetic energy? Did you take that into account?
 
TSny said:
Hello, and welcome to PF!Do both electrons end up with some kinetic energy? Did you take that into account?
Thanks for replying!
Oh I don't think I did. So it would be Ee1 = (1/2)mv^2 + (1/2)mv^2.
 
Yes. Are you assuming that the two electrons end up with the same speed? Can you justify that?
 
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