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Four masses $10\ \mathrm{g}$ each are tied together by $10\ \mathrm{cm}$ strings to make a square as shown. Two of the masses carry a charge of $2\ \mathrm{\mu C}$. The string between the two charged masses is cut and the system begins to move. What is the maximum speed of the masses in $\mathrm{m/s}$? Do not consider gravity or friction. You can imagine the masses to be on a horizontal frictionless table.

picture of four masses connected by strings

The answer key says that the two charges repel and they go on an infinite loop of oscillation. And it also points out that the center of mass does not move. What does the center of mass have anything to do with this problem?

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  • $\begingroup$ Hi and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ Apr 14 '16 at 14:23
  • $\begingroup$ I'm self-studying physics and I'm not asking you guys to do my homework problem. This is a problem from an online course on EDX and the answer key is also available on the website. Sorry if I violated any rules of the forum. $\endgroup$
    – Hello
    Apr 14 '16 at 14:29
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Apr 15 '16 at 7:15
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As written with the bottom two being charged, there is no motion because they are still tied together. Presumably you want the left two to be charged so they can move away from each other. The CM does not move because every force in the system is balanced by an opposite force-there is no net force on the set of masses. This observation is useful because it allows you to link the motion in the two axes. Right at the moment the strings are cut, the left masses are repelling each other and accelerating vertically away from each other. As they start to move, they will pull the right masses to the left and be pulled themselves to the right. We can relate the left/right motion to the vertical motion by the fact that the CM is stationary.

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  • $\begingroup$ If you read the problem statement, it explains what is going on: "The string between the two charged masses is cut". So there is a string joining the two charges, but then the string is cut so the charges can move away from each other. $\endgroup$ Apr 14 '16 at 17:32
  • $\begingroup$ @NowIGetToLearnWhatAHeadIs: the figure has two pairs of masses linked by strings, so I think it is after the strings are cut. Then it says the two bottom ones are charged, but they still have a string connecting them. That is the source of my suggestion that the leftmost two are charged, presuming the string connecting them has just been cut, as has the one on the right. $\endgroup$ Apr 14 '16 at 20:36
  • $\begingroup$ I believe the figure was made by LookAtTheBigPicture, not by the whoever originally made the question, so it may not be that high quality. In the text of the problem, it says that the strings make a square. It also says that the motion is oscillatory, which is not true in your interpretation. $\endgroup$ Apr 14 '16 at 21:32

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