Uniform Circular Motion of centrifuge

In summary, the conversation was about finding the number of revolutions per minute a sample makes in a centrifuge, given its radius and the fact that its centripetal acceleration is 6.25 times greater than the acceleration due to gravity. The equation for centripetal acceleration was discussed, as well as the calculation of angular velocity. The final conclusion was that the angular velocity can be found by taking the square root of the ratio of the centripetal acceleration to the radius and multiplying it by 2π.
  • #1
MetalCut
21
0
Hi there. I need some help with this question. Can anyone help me...

A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Suppose the centripetal acceleration of the sample is 6.25 X 103 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 5.00cm from the axis of rotation?

Any help would be appreciated.

Thanx
 
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  • #2
Could you please show some work or thoughts?

HINT: What is the equation for centripetal acceleration?

~H
 
  • #3
The equation is a = v2/r. But what do they mean when they say the centripetal acceleration is 6.25x10 3 times as large as the acceleration due to gravity?
 
  • #4
[tex]a = \left( 6.25\times 10^{3} \right)g[/tex]

~H
 
  • #5
So then that probably means that v2/r = (6,25x10 3)g

And the circumference of the circle its rotating in is 0,314m or 31,4cm
 
  • #6
But you want to find revolutions per minute, so your next step would be calculating the angular velcoity ([itex]\omega[/itex]). You will need to use;

[tex]v = \omega r[/tex]

~H
 
  • #7
But i can get (v) also with v=(2)(pie)(r)\T
So i still need T
 
  • #8
They are effectively the same thing, but you don't need to work out v;

[tex]a = \frac{v^2}{r}[/tex]

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

[tex]a = \frac{\omega^2 r^2}{r}[/tex]

[tex]\omega^{2} = \frac{a}{r}[/tex]

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

~H
 
  • #9
Thanx i think I've got it.
 

1. What is uniform circular motion in a centrifuge?

Uniform circular motion in a centrifuge refers to the motion of an object that is moving at a constant speed in a circular path around a fixed center point. In a centrifuge, this motion is used to separate substances of different densities by creating a centrifugal force.

2. How does a centrifuge create uniform circular motion?

A centrifuge creates uniform circular motion by spinning a container or rotor at a high speed. This rotation creates a centrifugal force, which pulls objects towards the outer edge of the container and creates a circular motion.

3. What factors affect the uniform circular motion in a centrifuge?

The speed of rotation, the radius of the container, and the mass of the objects being separated all affect the uniform circular motion in a centrifuge. A higher rotation speed or larger radius will create a stronger centrifugal force, while a heavier object will experience a greater force.

4. How is the velocity of an object in uniform circular motion calculated in a centrifuge?

The velocity of an object in uniform circular motion in a centrifuge can be calculated using the formula v = ωr, where v is the velocity, ω is the angular velocity, and r is the radius of the circular path.

5. What is the purpose of uniform circular motion in a centrifuge?

The purpose of uniform circular motion in a centrifuge is to separate substances of different densities by creating a centrifugal force. This is useful in many fields, such as medicine, where it is used to separate blood components, and in chemistry, where it is used to isolate different compounds.

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