- Wed May 14, 2014 8:35 pm
#188429
Okay, so I have a question about electrophysics.
On my second physics midterm, there was a question about an electron and proton at infinity at rest that accelerate toward each other and eventually meet.
The first part of the question was about which has a greater acceleration. Well, the electron does, because they exert an equal force on each other but the electron has a smaller mass.
The second was about which travels further before they meet. The electron again, because they have the same initial velocity (0 m/s) but the electron has a greater acceleration.
The third and last part of the problem is what confused me: which has a greater kinetic energy at the moment they meet?
Okay, so first try a work-based analysis (which is what the exam recommended, and the one I ended up going with in the end). By conservation of energy, the change in kinetic energy is equal to the work, which is equal to force*displacement. Well, they have the same force but the electron has a greater displacement, so it would have more final KE, right?
But then I did a potential energy analysis, and found that since they undergo the same change in potential energy (with an initial PE of 0 and a final of -ke^2/r_final), they must undergo the same change in kinetic energy, meaning they have the same KE at the end. What? I mean, this makes more sense from a conservation of energy standpoint (where did the extra work done on the electron come from, anyway?) but it's inconsistent with the work analysis. So, what's going on here? Cube? Anybody?
Thanks,
~dlgn
On my second physics midterm, there was a question about an electron and proton at infinity at rest that accelerate toward each other and eventually meet.
The first part of the question was about which has a greater acceleration. Well, the electron does, because they exert an equal force on each other but the electron has a smaller mass.
The second was about which travels further before they meet. The electron again, because they have the same initial velocity (0 m/s) but the electron has a greater acceleration.
The third and last part of the problem is what confused me: which has a greater kinetic energy at the moment they meet?
Okay, so first try a work-based analysis (which is what the exam recommended, and the one I ended up going with in the end). By conservation of energy, the change in kinetic energy is equal to the work, which is equal to force*displacement. Well, they have the same force but the electron has a greater displacement, so it would have more final KE, right?
But then I did a potential energy analysis, and found that since they undergo the same change in potential energy (with an initial PE of 0 and a final of -ke^2/r_final), they must undergo the same change in kinetic energy, meaning they have the same KE at the end. What? I mean, this makes more sense from a conservation of energy standpoint (where did the extra work done on the electron come from, anyway?) but it's inconsistent with the work analysis. So, what's going on here? Cube? Anybody?
Thanks,
~dlgn
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