1. A nanoscale cantilever can be used to measure the mass of DNA molecules. One oscillates...
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?
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,...
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,...
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5. A mass-spring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the mass is 0.50 kg, a) Write an equation for the position, velocity, and acceleration for the mass as a function of time b) find the maximum speed of the mass, and the maximum acceleratjon of the mass. c) Sketch a plot of the position of the mass vs time by labelling the...
14.4 A 3 kg mass oscillates on the end of a spring with an amplitude of 32 cm. a) If the maximum acceleration of the spring is 43.3 m/s2 , what is the spring constant of the spring? b) What is the frequency of the oscillation? c) If the spring was released at t = 0 s, how many complete oscillations occur in the first 10 s?
1) A 7.5kg mass attached to a spring with a spring constant of 365 N/m oscillates on a horizontal, frictionless track. Att 0, the mass is released from rest at x-2.32 cm. (That is, the spring is stretched by 2.32 cm.) (a) Determine the frequency of the oscillations. (b) Determine the maximum speed of the mass. Where does the maximum speed occur? (c) Determine the maximum acceleration of the mass. Where does the maximum acceleration occur? 2) A body is...
A 250 g mass is attached to a horizontal spring and oscillates with a frequency of 2.1 Hz. At one instant the mass is at -4.3 cm and has a horizontal velocity of 25 cm/s. A. What is the spring constant? B. What is the total energy of the oscillator? C. What is the period of oscillation? D. What is the amplitude? E. What is the maximum speed?
A 250 g mass is attached to a horizontal spring and oscillates with a frequency of 2.1 Hz. At one instant the mass is at -4.3 cm and has a horizontal velocity of 25 cm/s. A. What is the spring constant? B. What is the total energy of the oscillator? C. What is the period of oscillation? D. What is the amplitude? E. What is the maximum speed?
3. A 250 g mass is attached to a horizontal spring and oscillates with a frequency of 2.1 Hz. At one instant the mass is at -4.3 cm and has a horizontal velocity of 25 cm/s. A. What is the spring constant? B. What is the total energy of the oscillator? C. What is the period of oscillation? D. What is the amplitude? E. What is the maximum speed?
3. A 250 g mass is attached to a horizontal spring and oscillates with a frequency of 2.1 Hz. At one instant the mass is at -4.3 cm and has a horizontal velocity of 25 cm/s. What is the spring constant? B. What is the total energy of the oscillator? What is the period of oscillation? D. What is the amplitude? E. What is the maximum speed?