QUESTION $2($TOTAL: $25$ MARKS$)$

$($a$)$ Imagine that you are designing a digital weight balance using strain gauges with the simplest structure, as shown in Figure $1($a$).$ What is the right design of the Wheatstone bridge $($label out $\backslash (\backslash$mathrm$\{$R$\}\_\{1\},\backslash$mathrm$\{$R$\}\_\{2\},\backslash$mathrm$\{$R$\}\_\{3\},\backslash$mathrm$\{$R$\}\_\{4\}\backslash )$ in Figure$1($b$)?$

$(4$ marks$)$

Figure $1($a$).$ Structure of the weight balance and strain gauges,

Figure $1($b$).$ Wheatstone bridge

If the minimum detectable change of the output voltage $\backslash ((\backslash$Delta $\backslash$mathrm$\{$U$\})\backslash )$ is $\backslash (\backslash$Delta $\backslash$mathrm$\{$U$\}\_\{\backslash$min $\}\backslash ),$ what is the minimum measurable mass $\backslash (\backslash$mathrm$\{$M$\}\_\{\backslash$text $\{$min $\}\}\backslash )?$

$(5$ marks$)$

Given that the gauge factor is constant over temperature range of $\backslash (70\backslash$mathrm$\{$~K$\}-350\backslash$mathrm$\{$~K$\}\backslash ),$ if you bring this weight balance from Singapore to North Pole, will it be still accurate? Explain the reasons.

$(4$ marks$)$

Mention at least two possible error sources of the strain gauge measurement.

$(2$ marks$)$

$($b$)$ You would like to employ the digital image correlation $($DIC$)$ method to replace the strain gauges. To convince your boss, briefly describe the basic principles of strain measurement, experimental procedures, at least three major advantages, at least three major influence factors on the measurement accuracy, and at least three typical applications.

$(10$ marks$)$