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A large ant is standing on the middle of a circus tightrope that is stretched with tension T_s. The rope has mass per unit length mu. Wanting to shake the ant off the rope, a tightrope walker moves her foot up and down near the end of the tightrope, generating a sinusoidal transverse wave of wavelength lambda and amplitude A. Assume that the magnitude of the acceleration due to gravity is g.

What is the minimum wave amplitude A_min such that the ant will become momentarily weightless at some point as the wave passes underneath it? Assume that the mass of the ant is too small to have any effect on the wave propagation.
Express the minimum wave amplitude in terms of T_s, mu, lambda, and g.

This question makes no sense. Is the equations supposed to be negative or positive?

If the maximum acceleration is A*w^2 how can you equate that to g or -g?

  • Physics -

    Use the information on tension and density per length to get the wave propagation velocity, V.
    V = sqrt(T_s/mu)
    Then get the frequency of up-and-down motion from
    f = V/(lamda)

    The acceleration experienced by the ant it a = (2 pi f)^2*A

    The ant will become moomentarily weightless if a = g

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