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Question
The correct formula
The correct formula  
Hello there.

I am trying to work out how to calculate the maximum expansion and contraction of a steel beam as defined by the formula;

L = L0 et (I have also attached an image of the correct formula)

Where by L = Change in length L0 = original length  = 1.682 x 10-4
and t = temperature

Answer
When given the value of t, just put it into the equation.
This can be done since the values of L0 and alpha are known.

To find the maximum, take the derivative with respect to t.
That is, dL/dt = alpha*L0*exp(alpha*t).

Setting this to 0 gives no maximum since the exponential is never 0.

What this says is that the maximum is at the hottest temperature we can get without melting the metal, for the higher the temperature, the more we get.

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Scott A Wilson

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