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?

Answer 1

Mass of the rope m = 6.272 kg

Wavelength is equal to 6.25 m

Step-by-step 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* 9.8=1764N`

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

Velocity of wave is given by

`v=\sqrt(T)/(\mu )`

`150=\sqrt(1764)/(\mu )`

`\mu =0.0784m/kg`

Therefore mass of the rope

`m=\mu L=0.0784* 80=6.272kg`

Wavelength is equal to

`\lambda =(v)/(f)`

`\lambda =(150)/(24)=6.25m`