Chapter 13, Problem 74GP

BIO Weighing a Bacterium Scientists are using tiny, nanoscale cantilevers 4 micrometers long and 500 nanometers wide—essentially miniature diving boards—as a sensitive way to measure mass. An example is shown in Figure 13-38. The cantilevers oscillate up and down with a frequency that depends on the mass placed near the tip, and a laser beam is used to measure the frequency. A single E. coli bacterium was measured to have a mass of 665 femtograms = 6.65 × 10⁻¹⁶ kg with this device, as the cantilever oscillated with a frequency of 14.5 MHz. Treating the cantilever as an ideal, massless spring, find its effective force constant.

Figure 13-38 A silicon and silicon nitride cantilever with a 50-nanometer gold dot near its tip. (Problem 74)