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 ( f S+V ) to the frequency without the virus ( f S ) is given by f S+V / f S = 1 / 1 + ( m V / m S ) , where m V is the mass of the virus and m 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 × 10 −16 g and a frequency of 2.00 × 10 15 Hz without the virus and 2.87 × 10 14 Hz with the virus. What is the mass of the virus, in grams and in femtograms?
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 ( f S+V ) to the frequency without the virus ( f S ) is given by f S+V / f S = 1 / 1 + ( m V / m S ) , where m V is the mass of the virus and m 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 × 10 −16 g and a frequency of 2.00 × 10 15 Hz without the virus and 2.87 × 10 14 Hz with the virus. What is the mass of the virus, in grams and in femtograms?
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
f
S+V
/
f
S
=
1
/
1
+
(
m
V
/
m
S
)
, where mV is the mass of the virus and mS 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 × 10−16g and a frequency of 2.00 × 1015 Hz without the virus and 2.87 × 1014 Hz with the virus. What is the mass of the virus, in grams and in femtograms?
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 w =
1660 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is Ymax = A = 0.099 meters.
Simple
Harmonic
Motion
wrist
pin
500 grams
Crankshaft
A (top of stroke)
B (midpoint)
-C (bottom of stroke) y=-A
y=+A
Determine all the following:
The angular frequency in proper units w =
The period of the piston, T =
The frequency of the piston, f =
The maximum velocity of the piston, Vmax =
meters/sec
The piston velocity when y = 58% of full stroke, v(y = 0.58 Ymax) =
seconds
Hz
rad/sec
meters/sec
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/sec
The figures show a properly inflated tire and an underinflated tire of the same car.
Estimate the percent change of the period of the underinflated tire compared to the properly inflated tire.
Estimate the distance this car would have to travel for the difference between the numbers of turns of the two wheels to be equal to one turn.
Which will undergo more turns, the underinflated or the properly inflated tire?
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