Stiffness of a single interatomic spring PLEASE HELP

In summary, the stiffness of a single interatomic "spring" can be determined by observing the changes in length of a tungsten rod with a 119 kg mass attached to the bottom. The stiffness of the entire wire is 9.1826e4 and there are 1.015e13 side-by-side long chains of atoms in the wire. Each chain contains 9.96e9 interatomic bonds. The spring constant of a single atomic spring can be calculated by dividing the spring constant of a single chain (9.1826e4/1.015e13).
  • #1
luckyg14
19
0
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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  • #2


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
 
  • #3


I still don't understand where the numbers for the formula are coming from though
 
  • #4


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
 
  • #5


the spring constant is 9.1826e4?
 
  • #6


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:
  • #7


9.1826e4/1.015e13 ?
 
  • #8


nevermind it said that was wrong no matter which way I tried :(
 
  • #9


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
 

1. What is the stiffness of a single interatomic spring?

The stiffness of a single interatomic spring refers to the amount of force required to deform the spring by a certain distance. It is a measure of the spring's resistance to deformation and is typically expressed in units of force per distance, such as N/m or N/mm.

2. How is the stiffness of a single interatomic spring calculated?

The stiffness of a single interatomic spring can be calculated using Hooke's Law, which states that the force applied to a spring is directly proportional to the distance it is stretched or compressed. The stiffness can be determined by dividing the force applied by the resulting displacement.

3. What factors affect the stiffness of a single interatomic spring?

The stiffness of a single interatomic spring can be affected by various factors such as the material properties of the spring, its length, and the number of atoms in the spring. Additionally, the stiffness can also be influenced by external factors such as temperature and applied forces.

4. Why is the stiffness of a single interatomic spring important?

The stiffness of a single interatomic spring is important because it affects the overall mechanical properties of a material. It can determine how much a material can be stretched or compressed without breaking and can also impact its strength and elasticity.

5. How does the stiffness of a single interatomic spring relate to the stiffness of a material?

The stiffness of a single interatomic spring is directly related to the stiffness of a material. In a solid material, the individual interatomic springs are connected, and their stiffness values are combined to determine the overall stiffness of the material. Therefore, the stiffness of a single interatomic spring can significantly impact the stiffness of a material.

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