Need help with centripetal acceleration problem.

  • Thread starter Imperil
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  • #1
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PROBLEM
A biophysicist wants to separate sub-cellular particles with an analytic ultracentrifuge. The biophysicist must determine the magnitude of the centripetal acceleration provided by the centrifuge at various speeds and radii.

Calculate the magnitude of the centripetal acceleration at 8.4cm from the centre of the centrifuge when it is spinning at 6.0 x 10^4rpm. Express your answer in terms of g (acceleration due to Earth's gravity).

MY ANSWER
r = 0.84m
f = 6.0 x 10^4rpm = 1000s

ac = 4pi^2rf^2
= 4pi^2(0.84m)(1000s)^2
= 3.32 x 10^7 m/s^2

So now that I have the centripetal acceleration I'm unsure of how to express my answer in terms of g as per the second part of the question. What I did was the following:

ac / g
3.32 x 10^7 m/s^2 / 9.8 m/s^2 = 3.39 x 10^6 m/s^2

but I am second guessing this because I really have no idea why I dividedt he acceleration by the acceleration of earths gravity. Could somebody shed some light on this and if I am wrong?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
8
ac / g
3.32 x 10^7 m/s^2 / 9.8 m/s^2 = 3.39 x 10^6 m/s^2

You have to wright the answer as
(ac / g)*g
3.32 x 10^7 m/s^2 / 9.8 m/s^2 = (3.39 x 10^6 )g. That is whar required.
 
  • #3
Shooting Star
Homework Helper
1,977
4
Express your answer in terms of g (acceleration due to Earth's gravity).

ac = 4pi^2rf^2
= 4pi^2(0.84m)(1000s)^2
= 3.32 x 10^7 m/s^2

So now that I have the centripetal acceleration I'm unsure of how to express my answer in terms of g as per the second part of the question. What I did was the following:

ac / g
3.32 x 10^7 m/s^2 / 9.8 m/s^2 = 3.39 x 10^6 m/s^2

but I am second guessing this because I really have no idea why I dividedt he acceleration by the acceleration of earths gravity. Could somebody shed some light on this and if I am wrong?

Some light has already been shed, but I'm just asking you this simple question: if ac was equal to, say, 4.1*9.8 m/s^2, how much would it be in terms of g?
 
  • #4
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Bro...The QUestion Stated that r=8.4cm, so r=0.084m not r=0.84m...Correct that and so u r answer would be one decimal off....right answer would be ac= 3.32*10^6...in terms of g = 3.39*10^5 no unit.
 

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