Measure L the unstretched length of the rubber band by placing the band on a

# Measure l the unstretched length of the rubber band

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Measure L , the unstretched length of the rubber band by placing the band on a flat surface and put a ruler or pen on top so that it lies flat. Then use the travelling microscope to measure this horizontal length of the band. What do you find? Probably your data points lie on a gentle curve, not on a straight line at all — if this isn’t obvious, hold the graph nearly level with your eye and look along the line of points. With the increased precision of measurement, the elastic behaviour is clearly non-linear. Further investigation of the non-linear behaviour If the expression F = Kx is inappropriate, can we find a better description? Suppose the true relation is a power series: Note that we have divided the extension x by the original un-stretched length L to give the fractional extension, often called the strain — this ensures that every power term of x/L is dimensionless so the coefficients A , B , C , … all have the units of force. You have seen that the linear ‘law’, taking just the first term of the series, is quite a good first approximation, so let us investigate the effect of adding just the second ( quadratic ) term. Since x is much less than L this term will be much less than the first, even if the coefficients A and B are similar. Your results probably show that F increases slower than a straight line as the extension x increases, which we can achieve by making the coefficient B negative. If we also try putting A numerically equal to B we have the simplest possible non-linear expression: Tabulate ( x/L ) – ( x/L ) 2 and plot this as the ordinate versus the mass m as abscissa. Draw your own conclusions.
2–3 Laboratory exercise 2 Some final algebra Even more precise investigations have shown that the expression: is a good description of the elastic behaviour of rubber. Here S stands for the stretched length, L + x . By expanding this expression as a power series in x/L try to derive a series in which the simple quadratic expression you used above appears as the first two terms. You will need to use the binomial theorem in your expansion; it is as follows: where we must have y 2 < 1 and n can be positive or negative. How much more accurate would your measurements have to be if you wanted to show experimentally that the next (cubic) term in the expansion was needed? Hint: roughly estimate the size of this term for largest masses you have used.
3–1 Laboratory exercise 3 Laboratory Exercise 3 – NUCLEONIC MEASUREMENTS Introduction Experimental techniques in nuclear and elementary particle physics can be extremely complex, requiring expensive apparatus and sophisticated treatment of data. However many of the principles can be illustrated by measurements that use radioactive sources, fairly familiar apparatus, and only simple arithmetic to derive results. This exercise uses a sample of the radioactive isotope cobalt-60 ( 60 Co) and a Geiger counter to demonstrate the absorption of ! - rays; it also illustrates the treatment of errors due to the variability of repeated measurements.

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• Summer '09
• Electrical resistance, Electrical network, Voltage drop, Thermometer, Geiger tube

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