Respuesta :
Answer:
t = 0.657 s
Explanation:
First, let's use the appropiate equations to solve this:
V = √T/u
This expression gives us a relation between speed of a disturbance and the properties of the material, in this case, the rope.
Where:
V: Speed of the disturbance
T: Tension of the rope
u: linear density of the rope.
The density of the rope can be calculated using the following expression:
u = M/L
Where:
M: mass of the rope
L: Length of the rope.
We already have the mass and length, which is the distance of the rope with the supports. Replacing the data we have:
u = 2.31 / 10.4 = 0.222 kg/m
Now, replacing in the first equation:
V = √55.7/0.222 = √250.9
V = 15.84 m/s
Finally the time can be calculated with the following expression:
V = L/t ----> t = L/V
Replacing:
t = 10.4 / 15.84
t = 0.657 s
The time it takes for the resulting disturbance to reach the other end will be t = 0.657 s. Option b is correct.
What is tension force?
The tension force is described as the force transferred through a rope, string, or wire as it is pulled by opposing forces.
The tension force is applied along the whole length of the wire, pulling energy equally on both ends.
Given data;
M: mass of the rope = 2.31 kg
V: Speed of the disturbance
T: Tension of the rope = 55.7 N.
u: linear density of the rope
L:Distance between supports=10.4 m
The density of the rope is;
u = M/L
u = 2.31 / 10.4
u = 0.222 kg/m
The speed of the disturbance is found as;
[tex]\rm V=\sqrt{\frac{T}{u}}\\\\ V=\frac{55.7}{0.222} \\\\ V= 15.84 \ m/s[/tex]
Velocity is found as the ratio of the distance and time;
[tex]\rm V= \frac{L}{t} \\\\ t= \frac{10.4}{15.84} \\\\ t= 0.657 \ sec[/tex]
Hence, the time it takes for the resulting disturbance to reach the other end will be ,t = 0.657 s. Option b is correct.
To learn more about the tension force refer to the link;
https://brainly.com/question/2287912
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