| The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerati

Question

4 years ago

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| The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerati

ons, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. Suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples

Mathematics

1 answer:

LiRa [457] · Answer 1 · 2022-01-27T20:20:25+03:00

The net force on the rotor due to the unbalanced samples : <u>64.4 N</u>

<h3>Further explanation </h3>

Centripetal force is a force acting on objects that move in a circle in the direction toward the center of the circle

$\large{\boxed{\bold{F= \frac{mv^2}{R}}}$

F = centripetal force , N

m = mass , Kg

v = linear velocity , m/s

r = radius , m

The speed that is in the direction of the circle is called linear velocity

Can be formulated:

$\displaysyle v=2\pi.r.f$

r = circle radius

f = rotation per second (RPS)

The sample has a mass of 10 mg larger than the opposing sample. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm

Known

RPM = 70,000, convert to RPS = 70,000: 60 = 1166.6

r = 12 cm = 0.12 m

m = 10 mg = 10⁻⁵ kg

then

Linear velocity :

$\displaystyle v=2\times 3.14\times 0.12\times 1166.6\\\\v=879.15\:m/s$