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Bensky
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[SOLVED] HELP! Circular motion problem.
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 mm from the central spin axis, and if the machine hits 59000 revolutions per minute, what would be the centripetal force exerted on a giant amoeba of mass 1.0 x 10^-8 kg at the bottom of the tube?
t=period=1/frequency
r=radius
V=velocity
m=mass=1.0 x 10^-8 kg
V = (2*pi*r)/T
F=(mv^2)/r
r=.165m (converted to m from mm by dividing by 1000)
m=1.0 X 10^-8
f = 983.3 revolutions per second (I changed 59000 rpm to revolutions per sec. by dividing by 60)
T (period) = 1/983.3 ~= .001
V=(2*pi*r)/T
V= ((2*pi)*.165)/0.001
V= 1036.725576 m/s
F=(mv^2)/r
F=((1 x 10^-8)(1036.725^2)) / .165
F=.0651393 N
Now, I've checked my math several times, so I don't think there's a problem with that - I also think I have the correct formulas. I'm thinking this is either a rounding error or I have the period wrong.
The answers I have tried so far: .065, .0651, and .07 - all are wrong somehow.
Can anyone explain what I have done wrong?
Homework Statement
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 mm from the central spin axis, and if the machine hits 59000 revolutions per minute, what would be the centripetal force exerted on a giant amoeba of mass 1.0 x 10^-8 kg at the bottom of the tube?
t=period=1/frequency
r=radius
V=velocity
m=mass=1.0 x 10^-8 kg
Homework Equations
V = (2*pi*r)/T
F=(mv^2)/r
The Attempt at a Solution
r=.165m (converted to m from mm by dividing by 1000)
m=1.0 X 10^-8
f = 983.3 revolutions per second (I changed 59000 rpm to revolutions per sec. by dividing by 60)
T (period) = 1/983.3 ~= .001
V=(2*pi*r)/T
V= ((2*pi)*.165)/0.001
V= 1036.725576 m/s
F=(mv^2)/r
F=((1 x 10^-8)(1036.725^2)) / .165
F=.0651393 N
Now, I've checked my math several times, so I don't think there's a problem with that - I also think I have the correct formulas. I'm thinking this is either a rounding error or I have the period wrong.
The answers I have tried so far: .065, .0651, and .07 - all are wrong somehow.
Can anyone explain what I have done wrong?
Last edited: