Stiffness of a single interatomic spring PLEASE HELP

[luckyg14]

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

 

[ehild]

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

 

[luckyg14]

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

 

[ehild]

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

 

[luckyg14]

the spring constant is 9.1826e4?

 

[ehild]

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

 

[luckyg14]

9.1826e4/1.015e13 ?

 

[luckyg14]

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

 

[ehild]

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