(20 pts) A micromachined accelerometer is made of a silicon fixed-free cantilever (50-um long, 10-um wide,...

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(20 pts) A micromachined accelerometer is made of a silicon fixed-free cantilever (50-um long, 10-um wide, and 2-m thick) and a proof mass (weight: 1 mg) concentrated at the free end of the cantilever. A piezo-resistor is fabricated on the top surface at the fixed end. Its longitudinal gauge factor is 40. Also, the silicon material can withstand a tensile strain of no more than 0.2% before breaking. Suppose the self-weight of the silicon cantilever can be neglected, and the deformation of the cantilever stays in the linear region. (1) Assuming the Hook's law ( ) still holds for the cantilever, determine the maximum allowable stress in the cantilever right before it breaks (5 pts). (2) Calculate the sensitivity of the piezoresistor ((AR/R)/Acceleration) (15 pts). Hint: refer to the sensitivity analysis of accelerometers discussed in "piezoresistive sensors" (20 pts) A micromachined accelerometer is made of a silicon fixed-free cantilever (50-um long, 10-um wide, and 2-m thick) and a proof mass (weight: 1 mg) concentrated at the free end of the cantilever. A piezo-resistor is fabricated on the top surface at the fixed end. Its longitudinal gauge factor is 40. Also, the silicon material can withstand a tensile strain of no more than 0.2% before breaking. Suppose the self-weight of the silicon cantilever can be neglected, and the deformation of the cantilever stays in the linear region. (1) Assuming the Hook's law ( ) still holds for the cantilever, determine the maximum allowable stress in the cantilever right before it breaks (5 pts). (2) Calculate the sensitivity of the piezoresistor ((AR/R)/Acceleration) (15 pts). Hint: refer to the sensitivity analysis of accelerometers discussed in "piezoresistive sensors"