required information\ncentrifuges are commonly used in biological laboratories for the\nisolation and…

required information\ncentrifuges are commonly used in biological laboratories for the\nisolation and maintenance of cell preparations. for cell separation,\nthe centrifugation conditions are typically $1.00 \\times 10^{3}$ rev/min using a\nrotor of radius 5.50 cm.\n\nto pellet out virus particles and even to separate large molecules such as proteins,\nsuper-high-speed centrifuges called ultracentrifuges are used in which the rotor spins\nin a vacuum to reduce heating due to friction. what is the radial acceleration inside an\nultracentrifuge at 75,000 rev/min with an 5.50-cm rotor?\n$\\square \\times g$

required information\ncentrifuges are commonly used in biological laboratories for the\nisolation and maintenance of cell preparations. for cell separation,\nthe centrifugation conditions are typically $1.00 \\times 10^{3}$ rev/min using a\nrotor of radius 5.50 cm.\n\nto pellet out virus particles and even to separate large molecules such as proteins,\nsuper-high-speed centrifuges called ultracentrifuges are used in which the rotor spins\nin a vacuum to reduce heating due to friction. what is the radial acceleration inside an\nultracentrifuge at 75,000 rev/min with an 5.50-cm rotor?\n$\\square \\times g$

Answer

Explanation:

Step1: Convert units to SI

First, convert rotational speed to rad/s and radius to meters: Rotational speed: $75000 \frac{\text{rev}}{\text{min}} = 75000 \times \frac{2\pi}{60} \frac{\text{rad}}{\text{s}} = 2500\pi \frac{\text{rad}}{\text{s}}$ Radius: $5.50\ \text{cm} = 0.0550\ \text{m}$

Step2: Calculate radial acceleration

Use radial acceleration formula $a_r = \omega^2 r$: $a_r = (2500\pi)^2 \times 0.0550$ $a_r = 6250000\pi^2 \times 0.0550$ $a_r \approx 6250000 \times 9.8696 \times 0.0550$ $a_r \approx 3.43 \times 10^6\ \text{m/s}^2$

Step3: Divide by g to get factor

$g = 9.81\ \text{m/s}^2$, so the factor is: $\frac{a_r}{g} = \frac{3.43 \times 10^6}{9.81} \approx 3.50 \times 10^5$

Answer:

$3.50 \times 10^5$