Question

Zartan's vine, initially 6m long has a Young's modulus of .1 GN/m^2. If zartans weight causes a stress of 2.5*10^5 N/m^2, then

A)Determine the vnes change in length
B)the new length of the rope

Answer 1

\[l_{total} =l_o+\Delta l\]

Answer 2

\[Y=\frac{a}{\epsilon}=\frac{stress}{strain}=\frac{\frac{F}{A}}{\frac{\Delta l}{l_0}}\]

\[=\frac{Fl_0}{\Delta l A}\]

Answer 3

so now we have
\[Stress*\frac{\Delta L}{l_0}=Y\]
\[\frac{Y}{stress}=\frac{\Delta l}{l_0}\]
\[\frac{Yl_0}{stress}=\Delta l\]

Answer 4

\[Stress*\frac{l_0}{\Delta l}=Y\]
\[\frac{Stress*l_0}{Y}=\Delta l\]

\[\frac{2500000*6}{100000000}=.15m=15cm\]
\[l_{total}=l_0+\Delta l=6+.15=6.15m\]