How fast (in rpm) must a centrifuge rotate if a particle 9.00cm from the axis of rotation is to experience an acceleration of 115,000g's?
To find the required speed in rpm, we need to first convert the acceleration from g's to m/s^2.
1 g = 9.8 m/s^2
So, 115,000 g's = 115,000 * 9.8 m/s^2 = 1,127,000 m/s^2
Next, we need to calculate the radius of rotation in meters. Given that the particle is 9.00 cm from the axis of rotation, we convert it to meters:
9.00 cm = 0.09 m
Now, we use the centripetal acceleration formula:
a = (v^2) / r
Where:
a = acceleration (1,127,000 m/s^2)
v = velocity (unknown)
r = radius of rotation (0.09 m)
Rearranging the formula to solve for v:
v = sqrt(a * r)
v = sqrt(1,127,000 * 0.09)
v = sqrt(101,430)
v ≈ 318.76 m/s
Finally, we convert the velocity to rpm (revolutions per minute):
1 revolution = 2 * π * radius
1 minute = 60 seconds
rpm = (velocity / circumference) * (60 sec / 1 min)
circumference = 2 * π * r
rpm = (318.76 m/s) / (2 * π * 0.09 m) * (60 sec / 1 min)
rpm ≈ 12011.6 rpm
Therefore, the centrifuge must rotate at approximately 12,011.6 rpm for a particle located 9.00 cm from the axis of rotation to experience an acceleration of 115,000g's.