How Many Revolutions Per Second to Settle Red Corpuscles in a Centrifuge?

[hiddenlife5009]

Homework Statement

A sample of blood is placed in a centrifuge of radius 15.7 cm. The mass of a red corpuscle is 3.09×10-16 kg, and the magnitude of the force required to make it settle out of the plasma is 4.01×10-11 N. At how many revolutions per second should the centrifuge be operated?

Homework Equations

Fc = mv2/r

The Attempt at a Solution

Well I am not sure if the above equation actually helps with this question, but the equation can be rearranged to suit the values:

v = (Fc x r/m)^.5

From using this equation I can obtain the velocity which is 1427.39 m/s. My question is whether I am looking at this question with the completely wrong formula or am I on the right track? If I am on the right track, what would I go about doing next? I can't recall any ways of determining revolutions per second from velocity...

Any help would be most appreciated.

 

[Dick]

I think you dropped a decimal place in your calculation of v. 1.5km/sec is pretty fast! But to answer your question the circumference of a circle is 2*pi*r. If you cover n revolutions/sec then then your distance traveled is n*2*pi*r each second. What does distance traveled per second have to do with velocity?

 

[hiddenlife5009]

Sorry, I don't follow. I understand my fault with trying to find out the velocity, but I'm not sure where I go after finding the circumference, which is 98.65cm.

 

[nrqed]

Sorry, I don't follow. I understand my fault with trying to find out the velocity, but I'm not sure where I go after finding the circumference, which is 98.65cm.

You made a numerical error in your calculation..Recalculate the number and you will see that you are off by a factor of 10.

Now, to find the number of rebvolutions per second, you must simply use the fact that speed = total distance divided by time.

But the total distance is the number of turns times the circumference

Therefore speed = (number of turns * circumference)/ time

Isolate number of turns per unit time to find your answer.

 

[hiddenlife5009]

You made a numerical error in your calculation..Recalculate the number and you will see that you are off by a factor of 10.

Now, to find the number of rebvolutions per second, you must simply use the fact that speed = total distance divided by time.

But the total distance is the number of turns times the circumference

Therefore speed = (number of turns * circumference)/ time

Isolate number of turns per unit time to find your answer.

I have read your post over and over, and from what I understand, you mean the velocity I calculated was off by a factor of 10. I understand the whole method of finding the revolution per seconds now, but can't understand how I would go about obtaining a value for time and number of turns.

Therefore speed = (number of turns * circumference)/ time

 

[Dick]

If n is number of revolutions per second then distance traveled per second is n*2*pi*r. 'Distance traveled per second' is 'velocity'. So n*2*pi*r=v. You know v and r, so you can find n.

 

[nrqed]

I have read your post over and over, and from what I understand, you mean the velocity I calculated was off by a factor of 10. I understand the whole method of finding the revolution per seconds now, but can't understand how I would go about obtaining a value for time and number of turns.

Therefore speed = (number of turns * circumference)/ time

The point is that you cannot find a value for time by itself, nor a value for number of turns by itself. But that does not matter since you don't want neither fo those numbers, you just need the number of turns per second, you you just need to isolate the ratio turns/time which is speed/circumference. That was my point.

 

[cepheid]

The point is that you cannot find a value for time by itself, nor a value for number of turns by itself. But that does not matter since you don't want neither fo those numbers, you just need the number of turns per second, you you just need to isolate the ratio turns/time which is speed/circumference. That was my point.

This is an instance where the math might explain this more succinctly

v = \frac{2 \pi r}{T}

where v is the velocity, and T is the period of a revolution. You know v. You know 2 \pi r [/tex]. Therefore:<br /> <br /> \frac{v}{2 \pi r} = \frac{1}{T}<br /> <br /> The right hand side is, of course, what you are looking for. Anyway, this is exactly what nrqed said above.

 

[nrqed]

This is an instance where the math might explain this more succinctly

v = \frac{2 \pi r}{T}

where v is the velocity, and T is the period of a revolution. You know v. You know 2 \pi r [/tex]. Therefore:<br /> <br /> \frac{v}{2 \pi r} = \frac{1}{T}<br /> <br /> The right hand side is, of course, what you are looking for. Anyway, this is exactly what nrqed said above.

<br /> <br /> Well said. I guess I did not want to go this route because I di dnotfeel like exlaining that 1/period = number of revs/sec. I mean, it&#039;s not complicated but it sometimes confuses people the first time they are told this.<br /> <br /> Just to make it clear to the OP:<br /> <br /> T is the priod of revolution which is by definition the time for one revolution (or one rotation). Therefore, one way to express T is to say<br /> <br /> T = number of seconds / revolution<br /> <br /> Therefore, \frac{1}{T} = number of revolutions per second