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A tightrope walker wants to know the tension used to support the rope that is suspended between two poles. The rope is 18 m long and has a mass of 12 kg. She creates a wave pulse by tapping on one end of the rope and measures that it takes 2.7 s for the pulse to travel from one pole to the other. What is the tension in the rope?

Respuesta :

Answer:

T = 29.6 N

Explanation:

length of the rope is

L = 18 m

mass of the rope is

m = 12 kg

now we have

mass per unit length of the rope is given as

[te]\lambda = \frac{12 kg}{18 m}[/tex]

now time taken by wave to reach from end to other

[tex]t = \frac{L}{v}[/tex]

[tex]2.7 s = \frac{18}{v}[/tex]

[tex]v = 6.67 m/s[/tex]

now we have

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

[tex]6.67 = \sqrt{\frac{T}{0.67}}[/tex]

so we will have

[tex]T = 29.6 N[/tex]

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