In this example we will apply the equation v=FT to the simple case in which the

Question

In this example we will apply the equation v=FT to the simple case in which the tension in a rope is provided by the weight of a box. One end of a nylon rope is tied to a stationary support at the top of a vertical mine shaft that is 80.0 m deep (Figure 1) . The rope is stretched taut by a box of mineral samples with mass 20.0 kg suspended from the lower end. Another box of samples is hoisted up by the same rope. If the rope is shaken with the same frequency as before, and the wavelength is found to be 5.35 m , what is the mass of this box of samples?

Explanation / Answer

linear density, u = 2/80 = 0.025 kg/m

the speed of the wave is,

velocity = frequency * wavelength

v = 20*5.35 = 107 m/s

sqrt[(m*g)/u] = 107 m/s

m*g = u*1072

m = 0.025*11449/9.8

the mass of this box of samples, m = 29.21 kg

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