How fast must a cetrifuge rotate in order for a particle 9cm from the axis of rotation to experience an acceleration of 115000g's
115000*9.8=V^2/.09 solve for v.
If w is the angular rotation rate in radians per second, you must have
R*w^2 = 115,000 g = 1.127*10^6 m/s^2
w^2 = 1.252*10^7 (rad/s)^2
w = 3540 rad/s
That is about 34,000 rpm
To determine the speed at which a centrifuge must rotate for a particle at a distance of 9 cm from the axis of rotation to experience an acceleration of 115,000 g's, we can use the formula for centrifugal acceleration:
Centrifugal acceleration = (Rotation speed)^2 * Radius
Here, "g" represents the acceleration due to gravity.
First, we need to convert the acceleration from g's to meters per second squared (m/s^2). Since 1 g is approximately equal to 9.8 m/s^2, we will use that conversion:
Acceleration = 115,000 * 9.8 m/s^2
Next, we convert the particle's distance from centimeters (cm) to meters (m):
Radius = 9 cm = 0.09 m
Now we can rearrange the formula to solve for the rotation speed squared:
(Rotation speed)^2 = Acceleration / Radius
Plugging in the values:
(Rotation speed)^2 = (115,000 * 9.8 m/s^2) / 0.09 m
Simplifying this equation will give us the square of the rotation speed. Let's calculate it:
(Rotation speed)^2 = 1,187,777.78 m^2/s^2
Finally, to find the rotation speed, we take the square root of both sides of the equation:
Rotation speed = √(1,187,777.78 m^2/s^2)
Using a calculator, we can calculate the square root and find that the rotation speed is approximately 1,089 m/s.
Therefore, the centrifuge must rotate at a speed of approximately 1,089 meters per second in order for a particle 9 cm from the axis of rotation to experience an acceleration of 115,000 g's.