Centrifugal Force on blood

In summary: T} = \frac{1}{(number of seconds / revolution)} = \frac{1}{(number of seconds)} * (number of revolutions) = number of revolutions per second [/itex]Now, you already know that [itex] \frac{v}{2 \pi r} = number of revolutions per second [/itex] so just combine the two equations to get [itex] \frac{v}{2 \pi r} = \frac{1}{T} [/itex]or [itex] \frac{v}{2 \pi r} = \frac{seconds}{revolution} [/itex]
  • #1
hiddenlife5009
15
0

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.
 
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  • #2
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?
 
  • #3
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.
 
  • #4
hiddenlife5009 said:
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.
 
  • #5
nrqed said:
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
 
  • #6
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.
 
  • #7
hiddenlife5009 said:
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.
 
  • #8
nrqed said:
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

[tex] v = \frac{2 \pi r}{T} [/tex]

where v is the velocity, and T is the period of a revolution. You know v. You know [itex] 2 \pi r [/tex]. Therefore:

[tex] \frac{v}{2 \pi r} = \frac{1}{T} [/tex]

The right hand side is, of course, what you are looking for. Anyway, this is exactly what nrqed said above.
 
  • #9
cepheid said:
This is an instance where the math might explain this more succinctly

[tex] v = \frac{2 \pi r}{T} [/tex]

where v is the velocity, and T is the period of a revolution. You know v. You know [itex] 2 \pi r [/tex]. Therefore:

[tex] \frac{v}{2 \pi r} = \frac{1}{T} [/tex]

The right hand side is, of course, what you are looking for. Anyway, this is exactly what nrqed said above.

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's not complicated but it sometimes confuses people the first time they are told this.

Just to make it clear to the OP:

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

T = number of seconds / revolution

Therefore, [itex] \frac{1}{T} =[/itex] number of revolutions per second
 

1. What is centrifugal force on blood?

Centrifugal force on blood is the outward force that pushes blood away from the center of rotation in a centrifuge machine. This force is generated when the centrifuge spins at high speeds, causing the blood to separate into its different components based on their densities.

2. How does centrifugal force affect blood separation in a centrifuge?

Centrifugal force plays a crucial role in blood separation as it causes the denser components of blood, such as red blood cells and platelets, to move towards the bottom of the tube while the less dense components, such as plasma, move towards the top. This allows for easy separation and collection of the different components.

3. What factors can affect the centrifugal force on blood?

The centrifugal force on blood can be influenced by several factors, including the speed of the centrifuge, the size and shape of the centrifuge tubes, and the viscosity of the blood. The higher the speed and the larger the tube, the greater the centrifugal force will be. Blood with higher viscosity will also experience a stronger centrifugal force.

4. How is centrifugal force measured in a centrifuge?

The centrifugal force on blood is typically measured in multiples of the force of gravity, or g-force. This is because the centrifugal force is a relative force that is dependent on the force of gravity. For example, if a centrifuge is spinning at 1000 revolutions per minute (rpm) and has a radius of 10 centimeters, the centrifugal force would be approximately 200 g.

5. What are the applications of studying centrifugal force on blood?

Studying the centrifugal force on blood has many practical applications in the field of medicine and science. It is commonly used in laboratories to separate blood components for diagnostic tests and blood banking, as well as in research studies to investigate the properties of blood. Understanding the principles of centrifugal force can also aid in the development of new medical technologies and treatments.

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