Concept explainers
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
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
University Physics with Modern Physics (14th Edition)
Additional Science Textbook Solutions
College Physics (10th Edition)
University Physics (14th Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
College Physics: A Strategic Approach (3rd Edition)
Modern Physics
Physics: Principles with Applications
- A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.arrow_forwardA uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35arrow_forwardThe expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?arrow_forward
- Consider an undamped linear oscillator with a natural frequency ω0 = 0.5 rad/s and the step function a = 1 m/s2. Calculate and sketch the response function for an impulse forcing function acting for a time τ = 2π/ω0. Give a physical interpretation of the results.arrow_forwardWhat happens to the frequency of oscillations of a physical pendulum when the amplitude of oscillations increases by a factor of 2? O Oscillation frequency increases by a factor of 4. O Oscillation frequency decreases by a factor of 2. O Oscillation frequency stays the same. O Oscillation frequency increases by a factor of 2. What happens to the energy of oscillations in this case? O Energy of oscillations increases by a factor of 2. O Energy of oscillations increases by a factor of 4. O Energy of oscillations stays the same. O Energy of oscillations decreases by a factor of 2.arrow_forwardA spider can tell when its web has captured, say, a fly because the fly's thrashing causes the web threads to oscillate. A spider can even determine the size of the fly by the frequency of the oscillations. Assume that a fly oscillates on the capture thread on which it is caught like a block on a spring. What is the ratio of oscillation frequency for a fly with mass m to a fly with mass 2.5m?arrow_forward
- 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_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_forwardA spool of thread has an average radius of 1.00 cm. If the spool contains 62.8 m of thread, how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers. A) 3 140 B 1 000 C) 62 800 D 100arrow_forward
- Chapter 15, Problem 24 Z Your answer is partially correct. Try again. In the figure, two springs are joined and connected to a block of mass 40.3 kg that is set oscillating over a frictionless floor. The springs each have spring constant k = 242 N/m. What is the frequency (in Hz) of the oscillations? Number Units THz the tolerance is +/-2%arrow_forwardThe 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_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University