How do you work out Young's Modulus?

AI Thread Summary
To calculate Young's Modulus, one must determine the gradient of the stress-strain graph, which represents the ratio of stress to strain. The stress is measured in newtons per square meter (N/m²), while strain is dimensionless, being a ratio of lengths. Young's Modulus is expressed in pascals (Pa), which is equivalent to N/m². For accurate results, ensure that the stress and strain values are correctly plotted on the graph. Referencing resources like Wikipedia can provide additional clarity on the concept and calculations involved.
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I am really finding it hard to work out Young's Modulus.

I have my stress / strain graph

I was told I should apply a gradient on the graph to work out youngs modulus

The strain is in (m) and the stress is in (nm-2)

How do I work out the youngs modulus, and what unit of measurement would youngs modulus be in?
 
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Look in Wikipedia. It's a good explanation.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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