Centrifuges are commonly used in biological laboratories for the isolation and maintenance of cell preparations. For cell separation, assume centrifugation conditions that are 1.00 x 103 rpm using an 8.16-cm-radius rotor. What is the radial acceleration of material in the centrifuge under these conditions? Express your answer as a multiple of g. Do not enter unit.

Question

Centrifuges are commonly used in biological laboratories for the isolation and maintenance of cell preparations. For cell separation, assume centrifugation conditions that are 1.00 x 103 rpm using an 8.16-cm-radius rotor. What is the radial acceleration of material in the centrifuge under these conditions? Express your answer as a multiple of g. Do not enter unit.

Answer 1

1.00 * 103 rpm is a unit of angular velocity.

a = w^2 * r, where a is radial acceleration, and w is angular velocity, and r is the radius

You need to express your answer as a multiple of g, which is in units of m/s^2

Convert w = 1.00 * 103 rpm to rps (rotations per minute to rotations per second)

convert r = 8.16 cm to m

plug these numbers into the equation to get the acceleration, divide by g (9.8 m/s^2) to get answer

Answer 2

In reply to Jennifer, her explanation is CLOSE to be correct. Instead of converting rpm to rps, convert it to rad/s and use that as the velocity. To do this, multiply the rpm by 2π and then divide by 60. Use that and the radius in the formula then divide by 9.8 and you got it!

Answer 3

To find the radial acceleration, we can use the formula:

Radial acceleration = (angular velocity)^2 × radius

First, let's convert the angular velocity from rpm to radians per second. We know that 1 revolution is equal to 2π radians.

So, 1.00 x 10^3 rpm = 1.00 x 10^3 × 2π / 60 seconds

Now, let's calculate the angular velocity:

Angular velocity = 1.00 x 10^3 × 2π / 60 seconds

Next, we substitute the values into the formula:

Radial acceleration = (angular velocity)^2 × radius

Radial acceleration = [1.00 x 10^3 × 2π / 60 seconds]^2 × 8.16 cm

Now, let's simplify the calculation:

Radial acceleration = [1.00 x 10^3 / 60 seconds]^2 × 8.16 cm

Finally, to express the answer as a multiple of g, we can divide the radial acceleration by the acceleration due to gravity (g ≈ 9.8 m/s^2).

Radial acceleration (in units of g) = [1.00 x 10^3 / 60 seconds]^2 × 8.16 cm / (9.8 m/s^2)

Note: Make sure to convert the units appropriately (e.g., cm to meters).

After performing the calculations, you will have the value of the radial acceleration as a multiple of g.