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So the units for the modulus of elasticity can be expressed as PSI, Pa, or N/m $^2$. If you multiply the numerator and denominator of N/m $^2$ the unit for modulus of elasticity is then N-m/m $^3$, or J/m $^3$. But I don't believe J/m $^3$ is typically used for units of the modulus of elasticity. As I understand, the more common unit is the ...
Young's modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore, Young's modulus has units of pressure. From my reasoning if something is dimensionless, it should be a unitless ratio.
Confusion can often be resolved by examining the physical units in which quantities are expressed. Since stiffness and elasticity are expressed in different units, they cannot be the same thing. You are correct in believing that elasticity is a property of a material, while stiffness is a property of an object/material combination.
To get the spring constant of a given spring you divide this constant (in N) by the spring length. So, a longer spring has a lower k, it is less stiff than a short one, of the same type. This "modulus of elasticity" is not the same as Young's modulus which is a material property and has units of pascal (like pressure).
Is stiffness of a beam the product of Young's modulus and second moment of area? I read online that stiffness of a beam is function of the product of young's modulus and second moment of area. I cannot find any reference of the exact equation. Is it just the product of the young's modulus and the second moment of area or is there anything more?
For fluids such as gases and liquids, Young's modulus is zero; you won't encounter any resistance if you slowly pull on these materials uniaxially. However, the bulk modulus (i.e., the resistance one encounters when trying to compress these materials using pressure) is not zero; for an ideal gas, it is exactly equal to the pressure.
Shear strain does not change the volume of the material. Therefore, the shear modulus measures how easy it is to change the shape of an object (i.e. how rigid it is) while Young's modulus or the elastic modular measures how easy it is to stretch the object (i.e. how elastic it is).
Find the modulus of elasticity of the spring.' is a problem I've been asked to solve, and I've never seen a problem of this style before. I'm aware the modulus = stress/strain, but I don't know how to find stress without knowing the cross-sectional area. Any help would be much appreciated, thanks in advance.
$\begingroup$ This is a good answer, but I think it would be good to also point out that, depending on the geometry and the mode of vibration, moduli other than Young's modulus (e.g. the shear and uniaxial strain moduli, which for isotropic materials can be expressed in terms of E and the Poisson ratio) will come into play.
Consider a cube of unit dimensions. Let $\\alpha$ and $\\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying unit tension - 1) At one edge: Young's mo...