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$\bullet$ $\bullet$ 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 $\left(f_{\mathrm{s}+\mathrm{v}}\right)$ to the frequency without the virus $\left(f_{\mathrm{s}}\right)$ is given by the formula$$\frac{f_{\mathrm{S}+\mathrm{V}}}{f_{\mathrm{S}}}=\frac{1}{\sqrt{1+\frac{m_{\mathrm{v}}}{m_{\mathrm{S}}}}},$$where $m_{\mathrm{v}}$ is the mass of the virus and $m_{\mathrm{s}}$ is the mass of the silicon sliver. Notice that it is not necessary to know or measure the force constant of the spring. (b) In some data, the silicon sliver has a mass of $2.10 \times 10^{-16} \mathrm{g}$ and a frequency of$2.00 \times 10^{15} \mathrm{Hz}$ without the virus and $2.87 \times 10^{14} \mathrm{Hz}$ with the virus. What is the mass of the virus, in grams and femtograms?

(a) $\frac{f_{5}+v}{f_{s}}=\frac{1}{\sqrt{1+\frac{m x}{m_{s}}}}$(b) $m_{v}=99.88 \times 10^{-19} \mathrm{kg}=99.88 \times 10^{-16} \mathrm{g}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Rutgers, The State University of New Jersey

University of Sheffield

McMaster University

Lectures

04:12

In physics, potential ener…

02:18

In physics, an oscillation…

05:08

BIO Weighing a Virus. In F…

03:13

In February 2004, scientis…

03:28

Refer to the following dat…

03:37

07:48

The preceding problems in …

04:15

CALC A Spring with Mass. T…

06:03

It has recently become pos…

05:58

06:51

$\textbf{Longitudinal Wave…

04:04

Suppose an object of mass …

09:45

We usually ignore the kine…

16:16

An aging Hollywood actor (…

07:26

In your physics lab, an os…

06:59

Vibrations of a spring Sup…

04:34

In someone infected with m…

05:49

0:00

In someone affected with m…

06:53

(II) A mass $m$ on a frict…

06:46

For a certain oscillator t…

03:02

A mass $m$ is attached to …

I guess so. For question one, we to show the ratio is f s plus we over Fs is equal to one over square room one plus m v O M s first we know the frequency is equal to one over to buy Times Square. Okay, over and square. Okay. Over amnesty. Angular frequency. Omega Omega. You whoever told by Stevie Okay, And that's out of the equation was coming from. So first, the frequency with wires is equal to want to buy. I asked Square Okay, over M s class, a massive virus and f aster. Just simply people wanted to apply Times Square. Okay, Over m s. Therefore, I've as plus we over address. Will you quit? Well over two pi square. Okay. Over m s plus and we over a 1/2 pi times Square. Okay. Over M s. You see here a while until back. Cancel out. And this would just leave us one over. I'm sorry. Is will give us such thing here. Square room. Okay. Over m s. Plus we over square. Okay. Over m s. And this can be Do you drive it as square? Ooh que over m s plus and we over k over a mash, Okay? And this will give us k m s on me times I'm s over. Okay. Que Kenzo And this will give us m s over a mess. Plus And we well, we know that m s over m s plus and we is the reciprocal off m s plus and we over m s. Okay, So the square room I've m s over a mask Plus And we is people too A mess over m s less and we to the power of 1/2 Because square, we said to the powerful are half Okay, so this will give us m s plus and we over a mess to the power negative one which is the reciprocal off the M s plus and we over m s. And then there's a square root Remember so times the power of 1/2 and this will give us m s. Plus, I'm sorry. I'm sorry I'm bad over m s plus and we is equal to m s plus and we over m s to the power off. Negative will half, which is one over square room. I know what I mean. Jump to the next page is coming. Probably here. So this will give us a mask over M s plus and we is equal to one over square root a mask. Plus and we over m s. Okay. And this will give us one over square. Oh, m s over m s class and we over m s so I m s over m s is one. So eventually, you we go to one over I m I'm sorry. While we're square Ooh, one plus and we over a mess. So the frequency with virus over frequency without a virus is you go to one over square one, plus m we over a mess. Okay, so full question be he was asking us. Well, this is a massive virus. So from his equation, f s plus, we over f s is equal to one over square along costs, and we over a mess. Okay, So, looking for em, we So if we do some random here, which will get m v is equal to and this over, uh, as plus we over fs. The whole thing's where minus a mess so far on the question a mess was given us 2.1 times potential power public Nephew, 16 grams and FS Plus we was given as to going a four times potential Paolo, 14. Hers FS is equal to 2.0 times potential problem anteing hers. Okay, so if we plug in abounding, we'll get and we is equal to to a 0.1 times 10 to the power nuggets 16 grams over to appoint a four times intentional about Ford's he hers over. You're going? Oh, Central, about 15. Hers. The whole thing square. Mine's a mass which is to going one times. Look attends about negative 16 grams and this will give us the massive virus is equal to 99 times. Tend to about naked 16 grams, which is 99 I want a cars potential Negative 31. I'm sorry. Not there. You, I think so. Times potential negative one pentagrams. Okay, because one grams is able to 10 to the power 15 offensive worms. Okay. And that's the answer for this question. Thank you

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