You are to use a long, thin wire to build a pendulum in a science museum The wire has an unstretched length of $20\mathrm{.}0$ m and a circular cross section of diameter $0\mathrm{.}860$ mm ; it is made of an alloy that has a large breaking stress. One end of the wire will be attached to the ceiling, and a $8\mathrm{.}50$ kg metal sphere will be attached to the other end. As the pendulum swings back and forth, the wire I$\text{'}$s maximum angular displacement from the vertical will be $36\mathrm{.}0.$ You must determine the maximum amount the wire will stretch during this motion. So$,$ before you attach the metal sphere, you suspend a test mass $($mass $m)$ from the wire' $$ s lower end. You then measure the increase in length $l$ of the wire for several different test masses. $($Figure $1),$ a graph of $l$ versus $m,$ shows the results and the straight line that gives the best fit to the data. The equation for this line is $l=(0\mathrm{.}422m\frac{m}{k}g)m.$

Figure

$1$ of $1$

Part A

Assume that $g=9\mathrm{.}80\frac{m}{s^2},$ and use the graph to calculate Young' $s$ modulus $Y$ for this wire.

Express your answer with the appropriate units.

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Part B

You remove the test masses, attach the $8\mathrm{.}50$ kg sphere, and release the sphere from rest, with the wire displaced by $36\mathrm{.}0.$ Calculate the amount the wire will stretch as it swings through the vertical. Ignore air resistance

Express your answer with the appropriate units.

$l=$

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