Velocity of two masses due to electric potential energy

[Jaccobtw]

Homework Statement

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

Relevant Equations

U = kq/r
KE = 1/2mv^2

We can find the potential energy by finding the potential difference between the two masses. the minimum distance between the two masses is 10 cm. The maximum is 30 cm because they can be 3 string lengths apart as they repulse each other once the string is cut.

So, to get potential difference $$k_e q (\frac{1}{0.1} -\frac{1}{0.3})$$

Multiply by the other charge to get potential energy:

$$k_e q_1 q_2 (\frac{1}{0.1} -\frac{1}{0.3})$$

Set equal to 1/2 mv^2 and solve for velocity

I get about 6.9 m/s but this was wrong. Was my reasoning incorrect?

 

[PeroK]

How many masses move and how do they move relative to each other?

 

[Jaccobtw]

How many masses move and how do they move relative to each other?

Two masses move away from each other

 

[PeroK]

Two masses move away from each other

There are four masses in the problem. All tied to each other.