# Dual electron repulsion (momentum question)

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1. Sep 24, 2016

### mikemartinlfs

This is a multiple choice question that, after one incorrect attempt, I got correct; however, I want to actually understand what the explanation means. I'm hoping someone here can help.

1. The problem statement, all variables and given/known data

Two electrons, each with mass m and charge q, are released from positions very far from each other. With respect to a certain reference frame, electron A has initial nonzero speed v toward electron B in the positive x direction, and electron B has initial speed 3v toward electron A in the negative x direction. The electrons move directly toward each other along the x axis (very hard to do with real electrons). As the electrons approach each other, they slow due to their electric repulsion. This repulsion eventually pushes them away from each other.

Which of the following statements about the motion of the electrons in the given reference frame will be true at the instant the two electrons reach their minimum separation? (see #2 for more on this)

2. The attempt at a solution

The answer to this was "Both electrons are moving at the same (nonzero) speed in the same direction." (I chose "Both electrons are momentarily stationary" initially).

MASTERINGPHYSICS SITE FEEDBACK:

If at a given moment the electrons are still moving toward each other, then they will be closer in the next instant. If at a given moment the electrons are moving away from each other, then they were closer in the previous instant. The electrons will be traveling in the same direction at the same speed at the moment they reach their minimum separation. Only in a reference frame in which the total momentum is zero (the center of momentum frame) would the electrons be stationary at their minimum separation.

This is the aspect I'm looking for help on
; it talks about reference frames and how the difference in which reference frame I'm using will change the answer here. Perhaps I'm confused by the concept of the reference frame to begin with, but can someone break this down for me?
Also, when the question says "in the same direction" do they mean "both moving towards each other" or "both in either the +x or -x direction"?

Thanks for any help; I want to actually understand this, not just get the right answer. (I know this isn't the usual format for these questions but this is an online course with a very unresponsive professor).

2. Sep 24, 2016

### PeroK

If you take the CoM (centre of momentum) reference frame, then they both start out with a speed of $2v$ towards each other and at their point of closest approach they are both stationary.

If you take the reference frame you are given, then the CoM frame is moving in the -ve x-direction at speed $v$ with respect to that frame.

Are you with me so far?

If so, you can try to calulate the speed of each electron in the original reference frame at the time of their closest approach.

PS a diagram combining the two reference frames may help.

3. Sep 24, 2016

### mikemartinlfs

I suppose I'm still getting hung up on the concept of the reference frame and how that affects the question; your explanation shows that the CoM "reference frame" would be one in which both are moving at the same speed. If their speeds differ, you're not in the "CoM Reference Frame", is that what you're saying?

Then, when you get to the 2nd part, the reference frame given, what exactly does it mean by "the frame is moving in the -ve direction"? This is where I'm getting a bit lost; I wasn't under the impression that the reference frame itself was moving, only that this was the perspective that you were viewing this interaction from (as a stationary viewer). This is where I seem to be getting lost...

4. Sep 24, 2016

### PeroK

In the CoM frame the two electrons must (at all times) be moving with an equal speed in opposite directions (this includes the special case where they are both at rest).

If two reference frames are not moving with respect to each other, then they are the same reference frame!

Consider two cars moving towards each other and a "stationary" pedestrian. The two drivers and the pedestrian all have their own reference frame, and gghey are all moving with respect to each other. They are all stationary in their own reference frame, but in no one else's.

5. Sep 24, 2016

### mikemartinlfs

Let me ask this: if someone was observing this interaction from a "stationary" position, are the two electrons moving at an equal speed? And the only thing that causes one to "move faster" is the specific reference frame we're currently at?

So that would mean that our reference frame is currently "moving" in the direction of B with a v?

And that, because of this "frame of reference movement", when the two reach their minimum separation, our frame of reference is still "moving" at a speed of v despite both of the electrons being stationary to the CoM frame; thus, they appear to be "moving" in the same direction (-v)?

This is just me trying to explain how I'm seeing it in my head, so please feel free to tell me I'm wrong (and how I'm wrong) or if I'm simply WAY off base here.

Thanks so much for your patience and help

6. Sep 24, 2016

### PeroK

Yes, except there is no such thing as absolutely at rest and absolutely moving at speed $v$. The electrons, nor any observer, can ever say that they are absolutely at rest; only that they are at rest in a particular reference frame.

This is what is meant by "all motion is relative".

Last edited: Sep 24, 2016
7. Sep 24, 2016

### mikemartinlfs

Thanks again for your help; I was getting incredibly frustrated at the seemingly cryptic feedback from the website. You've been amazing :)

8. Sep 24, 2016

### J Hann

Another way to look at this is the an elastic collision between 2 equal masses.
For an elastic collision of equal masses the relative speed of approach equals the relative speed of separation.
Thus the relative speed of approach is 4 V and the relative speed of separation is 4 V.
At their minimum separation they cannot be moving w.r.t. one another. (sort of implied in the "feedback")
What does conservation of momentum tell you about their momentum relative to the "certain" reference frame?

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