What is the spring constant for an elastic cord with varying weights?

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Homework Help Overview

The problem involves determining the spring constant of an elastic cord based on its elongation under varying weights. The original poster provides measurements of the cord's length under two different weights and attempts to calculate the spring constant using Hooke's Law.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Hooke's Law and the significance of the equilibrium position. Some question the original poster's method of averaging the spring constants derived from two different weights and lengths.

Discussion Status

There is ongoing exploration of the problem, with some participants providing insights into the importance of the equilibrium length and suggesting that certain values may cancel out. Others express uncertainty about their own related problems, indicating a broader discussion on the topic.

Contextual Notes

Participants note the lack of information regarding the cord's original length without any weight, which is crucial for accurate calculations. There is also mention of potential confusion regarding the relationship between force, spring constant, and displacement.

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Homework Statement


An elastic cord is 67 cm long when a weight of 57 N hangs from it and is 80 cm long when a weight of 79 N hangs from it. What is the "spring" constant of this elastic cord?



Homework Equations



F=-Kx

The Attempt at a Solution



I substituted the numbers into the formula for each set, like for the 0.67 m, i got 85.1 N/m and for the other i got, 98.8 N/m and then i averaged the two because i didn't know what else to do, so i got 92.0 N/m for the average but it's wrong. Please help me!
Thanks
 
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Remember in that equation that x is the distance from equilibrium

You don't know how long the cord was when there was nothing on it, so you're not going to have it but you're given two cases, so eventually it'll cancel out
 
i have a similar problem so i didnt want to start a new thread, i hope there arent any feelings of thread jacking, but my problem is that i have the force and the k constant and an original length but i need to find the final length. would it be the force added to the k * x or multiplied like this: (mg)*k(x_2-x_1)
 
i sense that i am completely off...i will rethink this and come back
 
Yo, to calculate the spring constant you just have to use the change in mass.

76N-57N=19N

the change in distance (delta x) is 80cm-67cm=13cm

change cm into meters dividing by 100

13cm/100=0.13m

now plug n chug

19N=-K*0.13m

divide 19N by 0.13m and you have your answer...

146.15 N/m is your spring constant
 

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