How Do You Calculate the Effective Stiffness of an Iron Bar?

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    Spring Stiffness
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SUMMARY

The effective stiffness of an iron bar can be calculated using the formula ks = F/x, where F is the force applied and x is the extension of the bar. In this discussion, a 234 kg mass causes a 1.22 cm elongation in a 2.4 m long iron bar with a square cross-section of 0.15 cm. The calculated effective stiffness is approximately 0.0046 N/m. Additionally, the speed of the wave traveling through the bar can be determined after striking it, which is essential for understanding wave propagation in solid materials.

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What is the Spring Stiffness?

1. One mole of iron (6.02x10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter. You have a long thin bar of iron, 2.4 m long, with a square cross section, 0.15 cm on a side.

You hang the rod vertically and attach a 234 kg mass to the bottom, and you observe that the bar becomes 1.22 cm longer. Calculate the effective stiffness of the interatomic bond, modeled as a "spring":

Next you remove the 234 kg mass, place the rod horizontally, and strike one end with a hammer. How much time t will elapse before a microphone at the other end of the bar will detect a disturbance?

Homework Equations


Youngs Modulus? or Hookes law?

The Attempt at a Solution


ks = F/x
and i tried using youngs modulus doing it the long way and i got .0046 still wrong
 
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You can solve it by ks=F/x, but what values are you using for F and x? And regarding part 2, at what speed does the vibrating wave travel?
 

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