Pulling a long molecule

Suppose that a long molecule is modeled by a one-dimensional string of beads with alternating charges +q,q,+q+q,-q,+q \ldots . The distance between the beads is d and its known that F0=14πϵ0q2d2=10N. F_{0}= \frac{1}{4\pi \epsilon_{0}} \frac{q^{2}}{d^{2}}=10 \textrm{N}. One end of the of the string is being pulled by a force (parallel to the molecule) that is slowly increasing with time. What is the maximum force Fmax F_{max} in Newtons so that the molecule does not break.

Details and assumptions

  • The following identity may be useful: n=1(1)n11n2=π212. \sum_{n=1}^{\infty} (-1)^{n-1} \frac{1}{n^{2}}=\frac{\pi^{2}}{12}.
  • Don't assume you know a priori between which bead the molecule breaks...
×

Problem Loading...

Note Loading...

Set Loading...