Weighing a Bacterium Scientists are using tiny, nanoscale cantilevers 4 micromet

Question

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. 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 780 femtograms = 7.80×1016 kg with this device, as the cantilever oscillated with a frequency of 15.4 MHz . Treating the cantilever as an ideal, massless spring, find its effective force constant. k=??N/m

Explanation / Answer

here values are

m = 7.8*10^(-16) kg

frequency f = 15.4*10^6 Hz

now using formula

f = (1/2*pi)*sqrt(k/m)

k = (2*pi)^2*f^2*m = (2*22/7)^2*(15.4*10^6)^2*7.8*10^(-16) = 7.3 N/m

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