One end of a nylon rope is tied to a brick wall. The rope is stretched horizontally, passed over a pulley 80 meters away, and weighted with

Question

One end of a nylon rope is tied to a brick wall. The rope is stretched horizontally, passed over a pulley 80 meters away, and weighted with a mass 180.0 kg at the end. Waves on the rope are measured, and found to travel at 150 m/s. What is the mass of the rope between wall and pulley? If the rope is shaken sideways at 24.0 Hz, what is the wavelength of the waves produced?

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RuslanHeatt 7 months 2021-07-20T20:49:06+00:00 1 Answers 5 views 0

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    2021-07-20T20:50:49+00:00

    Answer:

    Mass of the rope m = 6.272 kg

    Wavelength is equal to 6.25 m      

    Explanation:

    Length of pulley L = 180 M

    Mass at the end of pulley m = 180 kg

    Frequency is given f = 24 Hz

    Acceleration due to gravity g=9.7m/sec^2

    Tension T=mg=180\times 9.8=1764N

    Velocity of wave in the rope v = 150 m/sec

    Velocity of wave is given by

    v=\sqrt\frac{T}{\mu }

    150=\sqrt\frac{1764}{\mu }

    \mu =0.0784m/kg

    Therefore mass of the rope

    m=\mu L=0.0784\times 80=6.272kg

    Wavelength is equal to

    \lambda =\frac{v}{f}

    \lambda =\frac{150}{24}=6.25m

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