Stiffness of a single interatomic spring PLEASE HELP

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Homework Help Overview

The discussion revolves around determining the stiffness of a single interatomic bond in tungsten, using measurements from a tungsten rod subjected to a weight. The problem involves concepts from material science and mechanics, particularly related to spring constants and atomic structure.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between macroscopic spring constants and atomic spring constants, questioning how to derive the stiffness of a single interatomic "spring" from the overall properties of the tungsten rod. There are discussions about the configuration of springs in series and how this affects the overall spring constant.

Discussion Status

Some participants have provided calculations and insights into the relationship between the macroscopic spring constant and the number of atomic chains. However, there remains uncertainty regarding the correct method to calculate the stiffness of a single interatomic bond, with multiple interpretations being explored.

Contextual Notes

Participants note the importance of understanding how the number of atomic springs in series affects the overall stiffness, and there are indications of confusion regarding the application of formulas and the source of numerical values used in calculations.

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stiffness of a single interatomic "spring" PLEASE HELP

One mole of tungsten (6 1023 atoms) has a mass of 184 grams, and its density is 19.3 grams per cubic centimeter, so the center-to-center distance between atoms is 2.51 10-10 m. You have a long thin bar of tungsten, 2.5 m long, with a square cross section, 0.08 cm on a side.

You hang the rod vertically and attach a 119 kg mass to the bottom, and you observe that the bar becomes 1.27 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in tungsten.

1) What is the spring stiffness of the entire wire, considered as a single macroscopic (large scale), very stiff spring?
ks= 9.1826e4 (correct)

2) How many side-by-side atomic chains (long springs) are there in this wire? This is the same as the number of atoms on the bottom surface of the tungsten wire. Note that the cross-sectional area of one tungsten atom is (2.51 10-10)2 m2.
Number of side-by-side long chains of atoms = 1.015e13 (correct)

3) How many interatomic bonds are there in one atomic chain running the length of the wire?
Number of bonds in total length = 9.96e9 (correct)

4) What is the stiffness of a single interatomic "spring"?
ks,i = CANNOT FIGURE OUT
 
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Imagine you connect two identical springs in series. Both have spring constant k. Exerting some force F on one spring, it expands by ΔL=F/k. Exerting the same force at the connected springs, what is the overall change of length? So what is the spring constant of the "new" spring?

ehild
 


I still don't understand where the numbers for the formula are coming from though
 


In a chain of springs, the tension is the same for all of them so every spring stretches by the same amount.The changes of length add up.
What is the spring constant of a chain of n springs?

ehild
 


the spring constant is 9.1826e4?
 


luckyg14 said:
the spring constant is 9.1826e4?

Yes, it is the spring constant of 1.015e13 chains of atomic springs. Edit: And there are 9.96 ˙109 atomic springs in a chain.So what is the spring constant of a single atomic spring?


ehild
 
Last edited:


9.1826e4/1.015e13 ?
 


nevermind it said that was wrong no matter which way I tried :(
 


luckyg14 said:
9.1826e4/1.015e13 ?

That is the spring constant of a single chain, but it is made of 9.96 ˙109 atomic springs in series.

ehild
 

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