$(10$ pts$)$ Consider a strain gauge on a cantilevered beam, placed and oriented as shown

below. You can approximate the strain, $lon,$ at the position of the strain gauge as $lon=\frac{6FL}{Eb{h}^2}$

where for this problem:

$F=1N,$ Bending force, applied as shown in the above figure

$L=0\mathrm{.}1m,$ Length between location of applied force and location of the strain

gages $($assume that the strain gages are sufficiently close so as to

experience the same strain$)$

$E=69$GPa, Beam modulus of elasticity $($aluminum in this case$)$

$b=2\mathrm{.}5cm,$ Beam width

$h=3mm,$ Beam thickness

You may also assume the following:

Fixed $350$ ohm resistors are placed in positions $2,3,$ and $4$

SG$1$ has a nominal $($unstrained$)$ resistance of $350$ ohm and a gauge factor of $2$

Excitation voltages: $V_{in}^{+}=10V$ and $V_{in}^{-}=-10V$

For this contiguration, tind:

The change in resistance of the strain gauge:

The Wheatstone Bridge Output Voltage in mV :