It has recently become possible to "weigh" DNA molecules by
measuring the influence of their mass on a nano-oscillator. Figure
shows a thin rectangular cantilever etched out of silicon (density
2300 kg/m3) with a small gold dot at the end. If pulled down and
released, the end of the cantilever vibrates with simple harmonic
motion, moving up and down like a diving board after a jump. When
bathed with DNA molecules whose ends have been modified to bind
with gold, one or more molecules may attach to the gold dot. The
addition of their mass causes a very slight-but measurable-decrease
in the oscillation frequency. A vibrating cantilever of mass M can
be modeled as a block of mass 13M attached to a spring. (The factor
of 13 arises from the moment of inertia of a bar pivoted at one
end.) Neither the mass nor the spring constant can be determined
very accurately-perhaps to only two significant figures-but the
oscillation frequency can be measured with very high precision
simply by counting the oscillations. In one experiment, the
cantilever was initially vibrating at exactly 14 MHz . Attachment
of a DNA molecule caused the frequency to decrease by 56 Hz .
What was the mass of the DNA?
Express your answer to two significant figures and include the appropriate units.
mass=volume×density=length×breadth×thickness×density
(cantilever is in the form of rectangle).
Frequency of oscillation of loaded spring depends on mass so as mass increases frequency ofooscillation decreases.
It has recently become possible to "weigh" DNA molecules by measuring the influence of their mass...
It has recently become possible to "weigh" DNA molecules by measuring the influence of their mass on a nano-oscillator. Figure shows a thin rectangular cantilever etched out of silicon (density 2300 kg/m3) with a small gold dot at the end. If pulled down and released, the end of the cantilever vibrates with simple harmonic motion, moving up and down like a diving board after a jump. When bathed with DNA molecules whose ends have been modified to bind with gold,...
1. A nanoscale cantilever can be used to measure the mass of DNA molecules. One oscillates at 8.8 MHz with an amplitude of 5.0 nm (see example 14.8 in the book). A. What is the maximum speed of the end of the cantilever? B. What is the maximum acceleration of the end of the cantilever?
1. A nanoscale cantilever can be used to measure the mass of DNA molecules. One oscillates at 8.8 M Hz with an amplitude of 5.0 nm (see example 14.8 in the book). A. What is the maximum speed of the end of the cantilever? B. What is the maximum acceleration of the end of the cantilever?
mass vibrates on an ideal spring as illustrated below. The total energy of the spring is 100 J. What is the kinetic energy of the mass at point P, halfway between the equilibrium point and the amplitude? P Equilibrium A. 50 J B. 200 J C. 75 J D. 100 J E. 25 J When a weight Wis hanging from a light vertical string, the speed of pulses on the string is v. If a second weight Wis added without...
A mass vibrates on an ideal spring as illustrated below. The total energy of the spring is 100 J. What is the kinetic energy of the mass at point P, halfway between the equilibrium point and the amplitude? P Equilibrium A. 50 J B. 200 J C. 75 J D. 100 J E. 25 J When a weight Wis hanging from a light vertical string, the speed of pulses on the string is v. If a second weight Wis added...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated sludge operation that adversely affect effluent quality with origins in the engineering, hydraulic and microbiological components of the process. The real "heart" of the activated sludge system is the development and maintenance of a mixed microbial culture (activated sludge) that treats wastewater and which can be managed. One definition of a wastewater treatment plant operator is a "bug farmer", one who controls the aeration...