A large ant mass of m=2.8g is standing on the middle of a circus tightrope that

Question

A large ant mass of m=2.8g is standing on the middle of a circus tightrope that is streched with tension F=750N. The rope have a mass per unit length of mu=1.5kg/m. 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 lamda = 25m and amplitude 5cm.

A) what is the minimum apparent weight of the ant when the wave propagates along the rope?

B) What is the mininmum apparent weight weight of the ant when the wave propagates along the rope if the wavelength is reduced to 15m?

C) At which value of lamda will the ant be momentarily weightless at some point?

Explanation / Answer

speed of wave=sqrt(T/mu)=22.36m/s

frequency=v/lamda=0.8944 Hz

w=2pi*f=5.62rad/s

a)min. weight=mg-mAw^2=23N

b)w'=2pi*v/lamda'=9.37rad/s

min weight=mg-mAw'^2=15.2N

c)Wmin=mg-mAw^2=0

w=sqrt(g/A)=14rad/s=2pi*22.36/lamda

lamda=10.04m

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