(Solved): A force measurement system consists of a rectangular steel bar (Young's Modulus E= 200GPa, Poisson ...

A force measurement system consists of a rectangular steel bar (Young's Modulus $$E=$$ $$200\mathrm{GPa}$$, Poisson's Ratio $$v=0.3$$ ) with a strain gage (gage factor $$K=3$$ ) fixed to one side of the bar in longitudinal (parallel to bar axis) orientation as shown. You may assume the bar to be in a state of uniform axial load where Hooke's Law gives the relationship between applied Force $$(F)$$, cross-section area $$(A)$$, Young's modulus $$(E)$$, and longitudinal strain $$(?)$$ as: $$\frac{F}{AE}=?$$ The strain gage is wired as one leg of a quarter-bridge circuit having excitation voltage $$V_i$$ $$=9\mathrm{V}$$. A digital voltmeter having range of $$\pm 100\mathrm{mV}$$, resolution of $$1\mathrm{mV}$$, and accuracy of $$\pm 3\%$$ of full-scale is used to measure the bridge output voltage, $$V_o$$. The relationship between strain $$(?)$$ and output voltage is: $$V_o=\left(\frac{K{V}_i}{4}\right)?$$ The components taken together represent a force measurement system where the input quantity is force $$(F)$$ and the output quantity is voltage $$\left(V_o\right)$$. a) What is the measurement system sensitivity? Give both the numerical value and units. b) What is the measurement system resolution? Give both the numerical value and units. c) What is the measurement system range? Give both the numerical value and units.