Tension of String/ Mass question

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Homework Help Overview

The problem involves two masses hanging from a steel wire, with a wave pulse traveling along the wire. Participants are tasked with determining the mass of one of the objects based on the tension in the wire and the wave speed.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of tension using the wave speed and mass per unit length. There are attempts to apply Lami's theorem and to convert units correctly. Some participants question the original poster's calculations and assumptions regarding the mass of the wire.

Discussion Status

The discussion is ongoing, with participants providing different approaches to the problem. Some guidance has been offered regarding unit conversion and the application of Lami's theorem, but no consensus has been reached on the correct method or final answer.

Contextual Notes

There is a noted discrepancy between the original poster's calculated mass and the expected answer, prompting questions about potential errors in assumptions or calculations. The mass of the wire and the angle of inclination are also relevant factors under discussion.

neoking77
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Homework Statement


The figure shows two masses hanging from a steel wire. The mass of the wire is 60.0 g. A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms.

What is mass m?
knight_Figure_20_80.jpg

Homework Equations


v = sqrt(Ts/mu)

The Attempt at a Solution


T=mu*v^2

t = 0.024s
d = 4m
v = d/t = 166.666m/s

mu = m/L = 60g/8m = 7.5

T = 208331Nsin40 = mg
m = 208331Nsin40/g
m = 13.66

but the answer is 17.8kg. where did i go wrong?
 
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the tension that you get from

T=mu*v^2

(I get 209 N - it is 60 grams) is the x-component of the tension in the inclined part of the wire.
 
Convert 60 g to kg and try again.
 
By using Lami's theorem You can find tension across point 1 and 2.
T/cos40 = mg/sin40. Hence T = mg*cot40.
m = (7.5^-3*166.67^2)/9.8*cot40
= 17.8kg.
 

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