A test tube in a centrifuge is pivoted so that it swings out horizontally as the machine builds up speed. If the bottom of the tube is 165.0 mm from the central spin axis, and if the machine hits 53500 rev/min, what would be the centripetal force exerted on a giant amoeba of mass 8.00E-9 kg at the bottom of the tube?
To find the centripetal force exerted on the giant amoeba, we can use the formula:
F = m * ω² * r
where:
F is the centripetal force
m is the mass of the amoeba (given as 8.00E-9 kg)
ω is the angular velocity in radians per second
r is the radius from the central spin axis (165.0 mm or 0.165 meters)
First, we need to find the angular velocity (ω) in radians per second. We can convert the given speed from revolutions per minute (rev/min) to radians per second by using the conversion factor:
1 revolution = 2π radians
So, we have:
ω = (2π * 53500 rev/min) / (60 sec/min)
Now, let's plug in the values into the formula to calculate the centripetal force:
F = (8.00E-9 kg) * ((2π * 53500 rev/min) / (60 sec/min))² * 0.165 meters
Now, we can simplify the equation and calculate the result:
F = 8.00E-9 * (2π * 53500 / 60)² * 0.165
After performing the calculations, the value of the centripetal force exerted on the amoeba can be obtained.
To find the centripetal force exerted on the giant amoeba at the bottom of the test tube, we can use the formula for centripetal force:
F = m * ω^2 * r
Where:
F is the centripetal force
m is the mass of the giant amoeba
ω (omega) is the angular velocity in rad/s
r is the radius from the central spin axis
We're given:
m = 8.00E-9 kg (mass of the giant amoeba)
r = 165.0 mm = 0.1650 m (radius from the central spin axis)
ω = 53500 rev/min
First, we need to convert ω from rev/min to rad/s:
1 rev = 2π rad
1 min = 60 sec
ω = (53500 rev/min) * (2π rad/rev) * (1 min/60 sec)
ω = 5623.37 rad/s
Now, we can calculate the centripetal force:
F = (8.00E-9 kg) * (5623.37 rad/s)^2 * (0.1650 m)
F = 0.096 N
Therefore, the centripetal force exerted on the giant amoeba is approximately 0.096 N.