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BIO Weighing a Virus. In February 2004, scientists at Purdue University used a highly sensitive technique to measure the mass of a vaccinia virus (the kind used in smallpox vaccine). The procedure involved measuring the frequency of oscillation of a tiny sliver of silicon (just 30 nm long) with a laser, first without the virus and then after the virus had attached itself to the silicon.
The difference in mass caused a change in the frequency. We can model such a process as a mass on a spring. (a) Show that the ratio of the frequency with the virus attached (fS+V) to the frequency without the virus (fS) is given by
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- The figure below shows a piston from your car engine. Don't worry, you will not be required to understand an internal combustion engine for this problem. Instead, we simply notice that the up/down motion of the piston is exactly described as Simple Harmonic Motion. The tachometer on your dashboard tells you that your engine is turning at ? = 2600 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is ymax = A = 0.071 meters.Determine all the following:The angular frequency in proper units ? = _ rad/secThe period of the piston, ? = _ secondsThe frequency of the piston, f = _ HzThe maximum velocity of the piston, vmax = _ meters/secThe piston velocity when y = 42% of full stroke, v(y = 0.42 ymax) = _ meters/secarrow_forward5A = Material point of mass m moves under the influence of force F-kr = –krî With in other words, the mass m is at the tip of an isotropic harmonic oscillator with equilibrium position at the origin of the axes. a) Calculate the potential energy V(r) of m. b) To design qualitatively 1) the potential energy V(r) of the mass m, 2) its "centrifugal" dynamic energy (r) = 1² /2mr² where L is the measure of angular momentum of the mass m and r its distance from the origin of the axes, and 3) the active potential energy of U(r) = V (r)+ Vä(r). "arrow_forwardK ( thevine white 51649 1₁ Class Work ADVANCED PLACEMENT PHYSICS 1 EQUATIONS, EFFECTIVE ELECTRICITY MECHANICS acceleration A amplitude C. No - FM E e energy frequency f F = force K kinetic energy spring constam Wal- Langular mothentom (length P = power P momentum U 1.99 T= period wtime V b. Find the acceleration each mass. radius or separation W R-E! A 7. AV potential energy volume P-TAV R-ER What is the tension force in the rope? F 4 15 kg 1 = Jonash - speed work done on a system position scceleration w power charge 12 kg O 1. "A 12 kg load hangs from one end of a rope that passes over a small frictionless pulley. A 15 kg counterweight is suspended from the other end of the rope. The system is released from rest & time V a. Draw a free-body diagram for each object showing all applied forces in relative scale. Next to each diagram show the direction of the acceleration of that object. d. What distance does the 12 kg load move in the first 3 s? TEQUESEN What is the velocity of 15 kg…arrow_forward
- The question is whether these relationships are linear or non-linear, can you please inform me on how I'd be able to tell?arrow_forwardThere are three identical rods and each of the has a mass of 1 kg and length of 39.2 cm. They are used in constructing a rigid body as seen in the figure. What is the period of small oscillations if it was pivoted at an axis through P? Take note that the center of mass of the rigid body is at Q. L L You can choose your answer here: 1.26 s 0.51 s 0.85 s 0.20 s L/2 P Q L/2arrow_forwardTwo pendula are shown in the figure. Each consists of a solid ball with uniform density and has a mass M. They are each suspended from the ceiling with massless rod as shown in the figure. The ball on the left pendulum is very small. The ball of the right pendulum has radius 1/2 L.Randomized Variables L = 1.3 m a) Find the period T of the left pendulum for small displacements in s. b) Find the period T of the right pendulum for small displacements in s.arrow_forward
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