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M3 Hooke's Law help

Hi I've worked out the natural length and I've attached the answer, but I'm stuck on working out the modulus of elasticity.I've attached the solution and I'm confused about how they got that first line of working. pls help.

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Reply 1

Onlineslayer

Okay. You mean the equation

Tension = lambda * extension/ original length?

Reply 2

Onlineslayer

Young modulus Y = stress/strain

Stress = force/ Area = Tension / Area
Strain = extension/original length

Therefore;

Y = (Tension * OriginalLength) / (Area * extension)

Make T the subject.

T = (Y*Area) extension/OriginalLength

But for the string, Y and Area are both constants.

So let lambda = Y * Area.

Hence,

T = lambda * Extension/OriginalLength

Q.E.D

Reply 3

Onlineslayer

If your question was about the first line on the white paper.

It was obtained by subtracting equation * from equation **

I.e, the equation on the right side of the brown paper, minus the equation on the left side (4th line) on the brown paper also.

Kindly make your question clearer next time