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Centripetal Acceleration

  • Thread starter Jpyhsics
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  • #1
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Homework Statement


A centrifuge is a laboratory device used for spinning samples of material. In a blood centrifuge, a test tube is inserted at an angle θ=32.0° with respect to the vertical and the whole sample is spun at high speed. For a typical test that is l= 15.9 cm long and is spun in a centrifuge at a rate of 4316 rotations per minute, what is the centripetal acceleration experienced by the sample at a point x=9.93 cm from the rotation axis, as measured along the test tube? Express your answer in units of the standard gravity g. Thus, if your answer is 19.62 m/s2 = 2.00×9.81 m/s2, you would enter 2.00 into the box.

Homework Equations


a=v2/r
T=2πr/f
v=d/t

The Attempt at a Solution


First, I found the period
T=2π(15.9)/(4316/60)=1.3888
v=2π(9.93)/1.3888=71.9
a=(71.9)2/9.93

I dont think I did this correctly, as I didnt use the angle....
I have included a photo as well,
 

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Answers and Replies

  • #2
TSny
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Homework Equations


a=v2/r
T=2πr/f
v=d/t
The equation T=2πr/f cannot be correct as you can tell by doing a unit analysis of the equation.

3. The Attempt at a Solution
First, I found the period
T=2π(15.9)/(4316/60)=1.3888
v=2π(9.93)/1.3888=71.9
a=(71.9)2/9.93
You need to be clear on the meaning of r in the equations. You want the centripetal acceleration of a particular point in the test tube. Mark this point in your diagram and try to draw a representation of r in the diagram.
 
  • #3
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The equation T=2πr/f cannot be correct as you can tell by doing a unit analysis of the equation.


You need to be clear on the meaning of r in the equations. You want the centripetal acceleration of a particular point in the test tube. Mark this point in your diagram and try to draw a representation of r in the diagram.
So how what formulas would I have to use?
I would assume ac=v2/r? but what about the period (T)?
 
  • #4
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So how what formulas would I have to use?
Would I use the 15.9cm?
 
  • #5
TSny
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So how what formulas would I have to use?
You should be able to solve it using your two equations

a=v2/r
v=d/t

But if you have learned how to write centripetal acceleration in terms of angular velocity ω, you might find that to be a quicker way to the answer.
 
  • #6
TSny
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but what about the period (T)?
If the test tube makes 4316 revolutions in one minute, how much time does it take for it to make one revolution?
 
  • #7
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If the test tube makes 4316 revolutions in one minute, how much time does it take for it to make one revolution?
0.0139s per rotation?
 
  • #8
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0.0139s per rotation?
Oh I see how the angle relates now. I got an answer of 10749 m/s2. Thank you so much for your help! :)
 
  • #9
TSny
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Oh I see how the angle relates now. I got an answer of 10749 m/s2. Thank you so much for your help! :)
I think your answer is correct. Good work.
 

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