Hooke's Law and Young's Modulus

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marinacalder
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#1
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Hey guys! I'm a bit confused regarding formulae for the two...

when studying SHM the tension in a spring was F= (lambda)x/l which could be shortened as F=kx (what is the relation between k and lambda?)

and studying young modulus... F=kx is used to simplify E= Fl/Ax where E = young modulus- how do all of these variables relate to one another? what is k? what is lambda? WHAT IS GOING ON?!! xD

many thanks




ALSO;

for the energy stored for young modulus graph, it is area under graph, i.e. Fx/2. But since this is a straight line i thought hooke's law would apply, giving E= (lambda) x^2/2l (obtained by integrating T= (lambda)x/l
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RogerOxon
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(Original post by marinacalder)
Hey guys! I'm a bit confused regarding formulae for the two...

when studying SHM the tension in a spring was F= (lambda)x/l which could be shortened as F=kx (what is the relation between k and lambda?)
F=kx=\lambda\frac{x}{l}=\frac{\lambda}{l}x

\therefore k=\frac{\lambda}{l}

\therefore \lambda=kl

and studying young modulus... F=kx is used to simplify E= Fl/Ax where E = young modulus- how do all of these variables relate to one another? what is k? what is lambda? WHAT IS GOING ON?!! xD
For a wire or rod, you can calculate the spring constant from a few other variables. Young's modulus is stress / strain, whereas the spring constant is force / extension. You can therefore calculate either from the remaining variables.
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marinacalder
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(Original post by RogerOxon)
F=kx=\lambda\frac{x}{l}=\frac{\lambda}{l}x

\therefore k=\frac{\lambda}{l}

\therefore \lambda=kl


For a wire or rod, you can calculate the spring constant from a few other variables. Young's modulus is stress / strain, whereas the spring constant is force / extension. You can therefore calculate either from the remaining variables.
Oh thank you so much, this makes sense! You're explanation is so clear and to the point! Much appreciated!
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Physics Enemy
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(Original post by marinacalder)
Hey guys! I'm a bit confused regarding formulae for the two...

when studying SHM the tension in a spring was F= (lambda)x/l which could be shortened as F=kx (what is the relation between k and lambda?)

and studying young modulus... F=kx is used to simplify E= Fl/Ax where E = young modulus- how do all of these variables relate to one another? what is k? what is lambda? WHAT IS GOING ON?!! xD

many thanks
F/x = k = lambda/L = EA/L

That's 3 formulae linked together with proportionality constants k, lambda and E. Formulae apply when object behaves elastically i.e) obeys Hooke's Law.

k is stiffness constant (spring constant in context of springs). Represents stiffness of an object.

E is Young's Modulus. Represents stiffness of a material (not the object, by accounting for A and L).

Lambda is modulus of elasticity. Like E, but can include other moduli (shear, volumetric) in 2D/3D. E is a 1D tensile modulus. E has units Nm^-2, Lambda (as defined here) has units N.

(Original post by marinacalder)
ALSO;

for the energy stored for young modulus graph, it is area under graph, i.e. Fx/2. But since this is a straight line i thought hooke's law would apply, giving E= (lambda) x^2/2l (obtained by integrating T= (lambda)x/l
Energy = Fx/2 = (kx)(x/2) = (kx^2)/2 ... what you'd get when integrating F = kx.

Energy = Fx/2 = (lambda)(x/L)(x/2) = (lambda)(x^2/2L) ... what you'd get when integrating F = (lambda)(x/L).
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