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Scientists arc using tiny, nanoscale cantilevers 4
Chapter 13, Problem 79GP(choose chapter or problem)
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 \(\text {665 femtograms}=6.65\times 10^{-16}\ \mathrm {kg}\) 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.
Equation Transcription:
Text Transcription:
665 femtograms=6.65x10^{-16} kg
Questions & Answers
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 \(\text {665 femtograms}=6.65\times 10^{-16}\ \mathrm {kg}\) 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.
Equation Transcription:
Text Transcription:
665 femtograms=6.65x10^{-16} kg
ANSWER:
Step 1 of 2
The mass of the bacterium is given by,
The frequency of oscillation is given by,
