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| 183_notes:youngs_modulus [2021/02/18 20:40] – [Hanging a mass from a platinum wire] stumptyl | 183_notes:youngs_modulus [2021/02/18 20:41] (current) – [Young's Modulus] stumptyl |
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| $$k_{s,wire} = \dfrac{mg}{s} = \dfrac{(10kg)(9.81 m/s^2)}{0.001166m} = 8.41\times10^4 N/m$$ | $$k_{s,wire} = \dfrac{mg}{s} = \dfrac{(10kg)(9.81 m/s^2)}{0.001166m} = 8.41\times10^4 N/m$$ |
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| This is very large spring constant because the wire (taken as a whole) is very stiff. Note: the units of N/m for k. | This is very large spring constant because the wire (taken as a whole) is very stiff. //Note: the units of N/m for k.// |
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| ==== Finding the number bonds in the wire ==== | ==== Finding the number bonds in the wire ==== |
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| The value that we found for the interatomic spring stiffness of Platinum (41.52 N/m) is typical of most pure metals, which have a range from about 5 to about 50 N/m. | The value that we found for the interatomic spring stiffness of Platinum (41.52 N/m) is typical of most pure metals, which have a range from about 5 to about 50 N/m. |
| ==== Young's Modulus ==== | ===== Young's Modulus ===== |
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| Like density, the interatomic spring stiffness ($k_{s,interatomic}$) is an [[http://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Intensive_properties|intensive property]] of an object, it doesn't depend on the length or shape of the object. Other properties are [[http://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Extensive_properties|extensive]] such as mass, volume, and the spring stiffness of the whole wire ($k_{s,wire}$). Scientists and engineers will often work with intensive properties because they characterize the material and not the object. However, the interatomic spring stiffness is not a property that scientists and engineers often use. When discussing the compression and extension of materials, they often use the bulk modulus or [[https://en.wikipedia.org/wiki/Young%27s_modulus|Young's modulus]]. | Like density, the interatomic spring stiffness ($k_{s,interatomic}$) is an [[http://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Intensive_properties|intensive property]] of an object, it doesn't depend on the length or shape of the object. Other properties are [[http://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Extensive_properties|extensive]] such as mass, volume, and the spring stiffness of the whole wire ($k_{s,wire}$). Scientists and engineers will often work with intensive properties because they characterize the material and not the object. However, the interatomic spring stiffness is not a property that scientists and engineers often use. When discussing the compression and extension of materials, they often use the bulk modulus or [[https://en.wikipedia.org/wiki/Young%27s_modulus|Young's modulus]]. |
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| === Stress and strain === | ==== Stress and strain ==== |
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| [{{ 183_notes:mi3e_04-018.png?100|Hanging a mass $m$ on the end of a wire with relaxed length $L$ and cross-sectional area $A$ results in an elongation (stretch) $\Delta L$.}}] | [{{ 183_notes:mi3e_04-018.png?100|Hanging a mass $m$ on the end of a wire with relaxed length $L$ and cross-sectional area $A$ results in an elongation (stretch) $\Delta L$.}}] |