A rope of total mass m hnd length L is suspended vertically with an object of mass M suspended from the lower end. Find an expression tor the wave speed at any point a distance x from the lower end. and calculate the time needed for the transverse pulse to travel the length of the rope. The rope has a length of 39.2 m and a mass of 1.00 kg. Suspended object has a mass of 8.00 kg.

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aristocles aristocles · Answer 1 · 2019-08-23T03:55:22+02:00

Answer:

Part a)

[tex]v = \sqrt{xg + \frac{MLg}{m}}[/tex]

Part b)

t = 12 s

Explanation:

Part a)

Tension in the rope at a distance x from the lower end is given as

[tex]T = \frac{m}{L}xg + Mg[/tex]

so the speed of the wave at that position is given as

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

here we know that

[tex]\mu = \frac{m}{L}[/tex]

now we have

[tex]v = \sqrt{\frac{ \frac{m}{L}xg + Mg}{m/L}[/tex]

[tex]v = \sqrt{xg + \frac{MLg}{m}}[/tex]

Part b)

time taken by the wave to reach the top is given as

[tex]t = \int \frac{dx}{\sqrt{xg + \frac{MLg}{m}}}[/tex]

[tex]t = \frac{1}{g}(2\sqrt{xg + \frac{MLg}{m}})[/tex]

[tex]t = \frac{2}{9.8}(\sqrt{(39.2\times 9.8) + \frac{8(39.2)(9.8)}{1}})[/tex]

[tex]t = 12 s[/tex]