Respuesta :
Answer:
The wire should be tightened because the present tension is 532.54 N where the required tension is 800 N and the higher the tension the more tightening is required.
Explanation:
To solve the question
v = [tex]\sqrt{\frac{F_t}{\mu} } = \sqrt{\frac{L*F_t}{m} }[/tex] where
v = velocity of the pulse in the string = 46.154 m/s
[tex]F_t[/tex] = Required tension force = 800 N
m = Mass of the wire = 15 kg
L = length of the wire to be tension-ed = 60 m
Since the pulse travels twice the distance of 60 m in 2.6 s the velocity is given by
v = 2×60/2.6 = 46.154 m/s
Therefore making [tex]F_t[/tex] the subject of the formula and substituting the values, we have
[tex]F_t[/tex] = [tex]\frac{v^2m}{L}[/tex] =[tex]\frac{46.154^{2*15} }{60}[/tex] = 532.54 N
This means that, as it is, the present tension in the wire is 532.54 N which is less than  the required 800 N, therefore the wire should be tightened
The wire should be tightened because the current tension on the wire is less than the required tension.
The given parameters;
- Required tension on the wire, T = 800 N
- Distance traveled by the Pulse, d = 60 m
- Time of motion of the pulse, t = 2.6 s
- Mass of the wire, m = 15 kg
The speed of the wave as the pulse traveled from one pole to the other two times, is calculated as follows;
[tex]v = \frac{2d}{t} \\\\v = \frac{2 \times 60}{2.6} \\\\v = 46.154 \ m/s[/tex]
The tension created on the wire during the pulse motion is calculated as follows;
[tex]v = \sqrt{\frac{T}{m/L} } \\\\v ^2 = \frac{TL}{m} \\\\T = \frac{v^2 m}{L} \\\\T = \frac{(46.154)^2 \times 15}{60} \\\\T = 532.55 \ N[/tex]
The current tension on the wire (532.55 N) is less than the required tension of 800 N. Thus, the wire should be tightened.
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