I am currently enrolled in Physics 140, General Physics I, at the University of Michigan. As can be imagined, my professor, Dr. Yuri Popov, rarely discusses the physics of ants. But a week or so ago, he broke from this usual monotony to present the following problem:
An ant with mass m is standing peacefully on top of a horizontal , stretched rope. The rope has mass per unit length μ and is under tension F. Without warning, Cousin Throckmorton starts a sinusoidal transverse wave of wavelength λ propagating along the rope. The motion of the rope is in a vertical plain. What minimum wave amplitude will make the ant become momentarily weightless? Assume that m is so small that the presence of the ant has no effect on the propagation of the wave.
First, I take offense at the idea that an ant has “no effect” on anything, let alone the propagation of a sinusoidal transverse wave! But that aside, I have illustrated this problem below:
Unfortunately, I could not get a photo of Sir Francis Throckmorton, but I trust that this picture of Francis Walsingham will suffice. I also took the liberty of making the educated assumption that the ant in question is Cephalotes atratus, the gliding ant (shown here).
If one can ignore the animal cruelty manifest in this situation, one will find that the answer to this question is [gμ(λ^2)]/[4(π^2)F], where g is the force of acceleration due to gravity. But the real question is: why am I not studying for my Physics final occurring this Friday? One will not find an answer to this question.