PLEASE EXPLAIN HOW TO SOLVE THIS. IF YOUR SOLUTION INCLUDES CHANGING THE FRAME O

Question

PLEASE EXPLAIN HOW TO SOLVE THIS. IF YOUR SOLUTION INCLUDES CHANGING THE FRAME OF REFERENCE, PLEASE EXPLAIN WHY THAT WOULD WORK (I.E. WOULDN'T THERE BE A DISCREPENCY IN THE ADDED FORCE AND ENERGY?)

3.15. Two small balls of mass m, bearing a charge q each, are connected by a noncon- ducting thread of length 21. At a certain in- stant, the middle of the thread starts mov- ing at a constant velocity v perpendicular to the direction of the thread at the initial instant. Determine the minimum distance d be- tween the balls.

Explanation / Answer

By concept of relative motion, it is similar to a situation when middle point is held stationary but the balls given a velocity v.

Let the minimum distance be d.

By energy conservation, kq^2/d = kq^2/2l + 2* 0.5 mv^2

kq^2/d =  kq^2/2l + mv^2

d = kq^2/ [kq^2/2l + mv^2 ]

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