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deff fn [24]
3 years ago
5

A 3.47-m rope is pulled tight with a tension of 106 N. A wave crest generated at one end of the rope takes 0.472 s to propagate

to the other end of the rope. What is the mass of the rope (in kg)
Physics
1 answer:
konstantin123 [22]3 years ago
6 0

Answer:

The mass of the rope is 1.7 kg.

Explanation:

Given;

length of the rope, L = 3.47 m

tension on the rope, T = 106 N

period of the wave, t = 0.472 s

frequency of the is calculated as;

f = \frac{1}{t} \\\\f = \frac{1}{0.472} \\\\f = 2.1186 \ Hz

the speed of the wave is calculated as;

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

where;

v is speed of the wave = fλ

λ is the wavelength

μ is mass per unit length

f\lambda = \sqrt{\frac{T}{\mu} } \\\\f(2l) = \sqrt{\frac{T}{\mu} } \\\\2fl =  \sqrt{\frac{T}{\mu} } \\\\(2fl)^2 = \frac{T}{\mu}\\\\4f^2l^2 =\frac{T}{\mu}\\\\\mu = \frac{T}{4f^2l^2}\\\\\frac{m}{l} =  \frac{T}{4f^2l^2}\\\\m = \frac{T}{4f^2l}\\\\m = \frac{106}{4(2.1186)^2(3.47)}\\\\m = 1.7 \ kg

Therefore, the mass of the rope is 1.7 kg.

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