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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?

Respuesta :

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 [tex]g=9.7m/sec^2[/tex]

Tension [tex]T=mg=180\times 9.8=1764N[/tex]

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

Velocity of wave is given by

[tex]v=\sqrt\frac{T}{\mu }[/tex]

[tex]150=\sqrt\frac{1764}{\mu }[/tex]

[tex]\mu =0.0784m/kg[/tex]

Therefore mass of the rope

[tex]m=\mu L=0.0784\times 80=6.272kg[/tex]

Wavelength is equal to

[tex]\lambda =\frac{v}{f}[/tex]

[tex]\lambda =\frac{150}{24}=6.25m[/tex]

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