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Intuitively, you understand that it takes more force to break bigger things. This means that when we measure material properties, we need to normalize by the size of the sample we're using. Since we quantify stress as force applied to some cross-sectional area, we need to measure both force and area. Similarly, strain is deformation (change in length) relative to some baseline length, which we need to measure.
Strain's the easy part. The extensometer recorded the force it applied and the deformation (increase in sample length) this force produced. We're just going to use engineering strain (rather than true strain) because it's quite difficult to measure total sample length during the entire test. But we still need initial length. This you measured as the length of your algal sample between the extensometer's clamps. You'll recall inputting this value into the computer before it produced your stress/strain diagram.
Stress is more difficult to measure because you need to know the cross-sectional area of your sample before you performed your test. It wouldn't be such a good idea to cut your sample in half before you test it, so you need to use the relationship between length, area and volume to determine cross sectional area. If we can find the volume of our sample, we've measured its length, so we know its area (Volume = Length *Area).
Constants:
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r = Density
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m = Mass
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V = Volume
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g = Gravitational acceleration
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L = Length of sample
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A = Cross-sectional area of sample
To determine volume using buoyant weight (weight in water):
m*g = ( r sample - r water)*V*g = Buoyant Weight
Divide both sides by g*V:
r sample - r water = Buoyant Weight / (g*V)
r sample - r water = Buoyant Mass / V
r sample = Buoyant Mass / V + r water
We measured both the buoyant mass (the mass suspended in water) and the dry mass (mass on the scale).
Since Mass/Density = Volume,
Mass (sample on dry land, on scale) / r sample = Volume =
A * L
Divide by L and plug in the value you derived for the density of the sample:
Mass (on dry land) / [ ( Buoyant mass (in water) / V + r water ) * L] = A (the cross-sectional area of sample)
Now that you have a cross-sectional area and a force at breaking (or at least the highest force you applied), you can calculate maximum stress (that you applied or that the alga could survive). It might also be interesting to think about the relative stiffness and extensibility of the various weeds. You might compare the characteristics of your sample with those of other materials (silly putty, limpet shells, whatever you imagine might be interesting). If you're a little ambitious, look into the shape of the stress/strain curve and see if you can determine whether your weed is made from a perfectly elastic or plastic material, or something in between.
Last, but not least, it might be neat to compare the forces you predict your alga could survive to the wave speeds (and thus forces) we measured in the intertidal. (See Waves are a Drag .)
Back to Material Properties
copyright Elizabeth Nelson, Judith Connor 1999, 2000 Non-profit educational uses permitted.