Is the net force on an object in a spinning test tube zero?

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Homework Help Overview

The discussion revolves around the net force acting on an object placed in a spinning test tube within a centrifugal machine. Participants explore concepts related to centripetal acceleration and forces in non-inertial frames of reference.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants question whether the net force on the object is zero despite its motion in a circular path. There is exploration of the relationship between acceleration and net force, particularly in non-inertial frames. One participant presents a more complex scenario involving fluid dynamics and seeks assistance in deriving a specific expression for net force.

Discussion Status

The discussion is active, with participants providing insights about centripetal acceleration and the implications of being in a non-inertial frame. Some guidance has been offered regarding the relationship between mass, acceleration, and net force, but there is no explicit consensus on the initial question regarding the net force being zero.

Contextual Notes

Participants are navigating assumptions about forces in a rotating system and the effects of fluid dynamics on the net force experienced by the object. The original poster expresses uncertainty about how to approach the problem involving the displaced fluid volume.

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An object is put in a test tube . The test tube is put in a centrifugal machine where it spins around. Would it be correct to say that the net force on the object is zero since it is not moving. I know the test tube has a net inward force that makes it change direction. But the object wants to fly out of the tube but is stopped by the bottom of the test tube.

Am I totally wrong here?
 
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it is not moving

What?
 
What I meant is that the object doesn't accelerate. But then again it changes direction. A direct answer would be appreciated.
 
centripetal acceleration

An object spinning in a circle is most definitely accelerating! It is accelerating towards the center of the circle; this is usually called centripetal acceleration. And, since it is accelerating, there must be a net force pulling the object towards the center.
 
That's what I thought. But wasn't sure because the object isn't in an inertial frame of reference.
 
If an object isn't in an inertial frame of reference then pretty much by definition you will observe that a force is acting on it.
 
O.K. I think I understand this but the real problem I don't understand, here it comes.

An incompressible fluid with density rho is in a horizontal test tube of inner cross-sectional area A. The test tube spins in a horizontal circle with angular speed w. Gravitational forces are negligeble. An object of volume V and density RHOob has its center of mass at a distance Rcmob from the axis. Show that the net horizontal force on the object is rhoVw^2Rcm, where Rcm is the distance from the axis to the center of mass of the displaced fluid. I have already derived expressions for the pressure at a distance from the surface of the water, and for the pressure difference for a volume element of thickness dr. It seems to me that the net force on the object is the mass*acceleration of the displaced fluid volume.

I don't know how to treat this problem. I see the force as the mass*acceleration of the object + displaced water.


Could anyone please help me.
 
Swatch said:
It seems to me that the net force on the object is the mass*acceleration of the displaced fluid volume.
The net force on any object is its mass time its acceleration. This object is being centripetally accelerated, so [itex]F_{net} = m a_c[/itex].
 

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