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"You have a lightweight spring whose unstretched length is 3.28 cm.

You're curious to see if you can use this spring to measure charge.

First, you attach one end of the spring to the ceiling and hang a 2.57 g

mass from it. This stretches the spring to a length of 4.37 cm. You then

attach two small plastic beads to the opposite ends of the spring, lay

the spring on a frictionless table, and give each plastic bead the same

charge. This stretches the spring to a length of 3.78 cm. What is the

magnitude of the charge on each bead?"

So, after finding the spring constant using the mass hung from the

ceiling, we can calculate the restoring force of the spring in the

spring-2bead system. This restoring force must be equal to the electric

force exerted by the beads since the spring is at equilibrium. This is

the part that I'm having trouble with. Shouldn't the restoring force be

equal to 2x the electric force? Each bead will exert a force on the

other and cause each to stretch the spring in opposite directions. In other words, the electric force of each bead on the other (so there are two forces) is what actually causes the spring to stretch to its equilibrium length. If we calculate using only one electric force, aren't we making the assumption that one bead is held still in position?

The answer as it stands is found by equating the restoring force to only one electric force so where have I gone wrong?

Thanks.