A silicon micro-cantilever ( ) for a force sensor is to be made with length and width

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Torsion and bending of rods and beams

Problem

A silicon micro-cantilever (

E = 169\,\mathrm{GPa}

) for a force sensor is to be made with length

L = 200\,\mathrm{\mu m}

and width

b = 30\,\mathrm{\mu m}

, clamped at one end and free at the other, loaded at the tip. Slopes remain small and the beam's own weight is ignored. ((a)) Find the thickness

h

needed to give it a spring constant

k = 0.50\,\mathrm{N\,m^{-1}}

, using

k = Ebh^3/4L^3

. ((b)) With that thickness, find the maximum bending stress at the clamped root when a tip force

F = 1.0\,\mathrm{\mu N}

is applied, and state whether it remains below an allowable design stress of

300\,\mathrm{MPa}

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