# 9.25 a centrifuge takes up only 0.127 m of bench space

• MHB
• karush
$r = \dfrac{a_r}{\omega^2} = \dfrac{4100g}{\left(\dfrac{6830\cdot 2\pi}{60}\right)^2}$$r = \dfrac{4100g}{\left(\dfrac{6830}{30}\right)^2\pi^2}$$r = \dfrac{4100g}{\left(\dfrac{6830 \cdot 6830 \cdot 30}{30 \cdot 30}\right)\pi^2}$$r = \dfrac{4100g}{6830 \cdot 6830 \cdot \pi^2}$$r = \dfrac{4100 karush Gold Member MHB$\textsf{An advertisement claims that a centrifuge takes up only $0.127 m$ of bench space}\textsf{but can produce a radial acceleration of $4100 \, g$ at $6830 \, rev/min$}\textsf{a. Calculate the requested radius of the centrifuge}$OK the only thing I can guess here is$\frac{0.127}{2}$as max karush said:$\textsf{An advertisement claims that a centrifuge takes up only $0.127 m$ of bench space}\textsf{but can produce a radial acceleration of $4100 \, g$ at $6830 \, rev/min$}\textsf{a. Calculate the requested radius of the centrifuge}$OK the only thing I can guess here is$\frac{0.127}{2}$as max$a_r = r\omega^2 \implies r = \dfrac{a_r}{\omega^2}$you'll need to convert$\omega$given in rpm to rad/sec skeeter said:$a_r = r\omega^2 \implies r = \dfrac{a_r}{\omega^2}$you'll need to convert$\omega$given in rpm to rad/sec$r = \dfrac{a_r}{\omega^2}\\\textit {how do you cancel the units? }\\\begin{align} \displaystyle \frac{0.127 \, m}{2} &\ge \dfrac{4100 \, g}{(6830\cdot 2\pi\cdot 60)^2 \, rad/s}\\ 0.0635&\ge \frac{4100 \, g}{6.629849 \, rad/s}\\ 0.0635&\ge 6.184 \end{align}not! Last edited:\dfrac{6830 \, rev}{min} \cdot \dfrac{2\pi \,rad}{rev} \cdot \dfrac{1 \min}{60 \,sec} = \dfrac{683\pi}{3} \, \dfrac{rad}{sec}r = \left(4100g \, m/sec^2\right) \left(\dfrac{3}{683\pi} \, \dfrac{sec}{rad} \right)^2 \approx 0.0785 \, md = 2r \approx 0.157 \, m > 0.127 \, m$seems their "claim" is false ...$\dfrac{6830 \, rev}{min} \cdot \dfrac{2\pi \,rad}{rev} \cdot \dfrac{1 \min}{60 \,sec} = \dfrac{683\pi}{3} \, \dfrac{rad}{sec}$where do you get $$\displaystyle \dfrac{683\pi}{3}$$ Last edited:$\dfrac{6830}{1} \cdot \dfrac{2\pi}{1} \cdot \dfrac{1}{60} = \dfrac{6830 \cdot 2\pi}{60} = \dfrac{6830 \cdot \pi}{30} = \dfrac{683 \cdot \pi}{3}\$

## 1. What is a centrifuge?

A centrifuge is a laboratory instrument that uses centrifugal force to separate particles of different densities in a sample. It is commonly used for separating liquids from solids, or for isolating specific components of a mixture.

## 2. How does a centrifuge work?

A centrifuge works by spinning the sample at high speeds, causing the denser particles to move towards the outside of the sample and the lighter particles to stay closer to the center. This separation is aided by the use of centrifugal force, which is the outward force created by the spinning motion.

## 3. What is the significance of 9.25 in the statement "9.25 a centrifuge takes up only 0.127 m of bench space"?

The number 9.25 refers to the size or capacity of the centrifuge, which is measured in liters. This means that the centrifuge has a maximum capacity of 9.25 liters for the sample being processed.

## 4. Why is the amount of bench space taken up by a centrifuge important?

In a laboratory setting, bench space is a limited resource and efficient use of space is essential. This is why it is important for equipment, such as a centrifuge, to take up as little space as possible so that more experiments can be conducted simultaneously.

## 5. Are there different types of centrifuges?

Yes, there are different types of centrifuges, including microcentrifuges, refrigerated centrifuges, and ultracentrifuges. These differ in their speed, capacity, and temperature control capabilities, making them suitable for different types of samples and applications.

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