Center of mass and external forces in a closed system

[whozum]

I'm sitting in my car on a flat road while it is stationary. The only forces acting on my car for this exercise are gravity and the normal force, which add up to give no net external force on my vehicle and me. My center of mass is at a fixed point somewhere in the vehicle, and according to the principles of Newton's laws, this fixed point should not move unless an external force outside of the car acts on the vehicle. If I was to raise my right arm, or do so little as to move my finger, my center of mass surely enough has changed its position, however no external forces have taken any effect.

How is this explained?

 

[Cyrus]

Think of your arm as being a rigid body. And think of your tendon as being a hydrolic piston. That piston extends, and is connected to a part of your arm. It in turn raises your arm as well.
When looking at your whole body, you have made your free body diagram so that it makes the forces rasiing your arm internal. The "outside force" on your arm is your tendons/muscles flexing and contracting. So there is a net force on it, and it does raise. You also have a force on it when you lower your arm, becase your muscles retard gravity from allowing them to swing down fast and hurt yourself.


If you are worried about the forces on your arm, then your free body diagram should include ONLY your ARM.

 

[whozum]

Well my arm was just the hypothetical object, but anything else could be used instead. I remeber a long time ago someone asked a simliar question with regards to a fly flying around in the car. Would the wing muscles be the external force then?

 

[Cyrus]

Well, you have a wing. What are the forces acting on its wing. I believe its motion is quite complicated, it swings up/down and back/fourth simultaneously. So consider it ball and socket connected at the juncture between the body of the fly and the wing. It will support half the weight of the fly, so its got a force of w/2 at that point. Its very light weight compared to the body of the fly, so you can ignore the weight of the wing itself. Its gota overcome that w/2 force to stay up, and hover. That will act at the center of pressure of the wing. ( I THINK). And create a moment about that hinge point. But that moment is balanced by the other wing creating an equal and opposite moment on the other side of the fly since its symmetrical. And the movement of the wings has to be driven by a tendon or something of that nature, that makes the wing move up and down. Again, you could think of it like a hydraulic piston connected from the body to the wing, that forces up/down motion of the wing.

If you try looking at the whole fly in the car, it does you no good. All the driving forces are now internal to the fly. That tells you nothing. You have to "disect" the fly to see the forces where you are concerned.


(actually, the net torque on the whole fly is zero, which is what I wrote earlier; however, the torque on the wing is not zero, and results in it rotating up and back).

 

[whozum]

So a closed system isn't necessarily a literally CLOSED system, for example although you could put the car and me and the fly in a box and look at it from the outside, a force within the box can still be considered external?

 

[Cyrus]

I don't understand why you are calling it a closed system. I thought a closed system is one where energy is not exchanged with the environment. Maybe someone more qualified can tell you that. I am just looking at the places of interest by segmenting the body and making the appropriate free body diagrams to see what are the internal forces at work.

 

[whozum]

The way I'm looking at it is in reference to Newton's laws and the inability of a center of mass to move without an external force. For example the popular airplane that blows up midflight is another example. If it breaks into 3 pieces the center of mass of the plane will continue along the same path that it was going before the explosion purely because it was a closed system.

 

[Tide]

How is what explained? You define your closed system incorrectly then you're surprised by the result. The system includes the Earth which is pushing up on your car. The act of raising your finger caused you to push down on the Earth which had to move in the opposite direction to compensate. The center of mass of the real system did not move.

 

[whozum]

How is what explained? You define your closed system incorrectly then you're surprised by the result. The system includes the Earth which is pushing up on your car. The act of raising your finger caused you to push down on the Earth which had to move in the opposite direction to compensate. The center of mass of the real system did not move.

Isn't a system anything you define it to be? So if I did define the system the way I did, then the external force acting on the car would be the normal force from the earth?

What if the motion was horizontal? for example shifting my finger to the right. Would it then be the friction force stopping the car from moving to the left?

 

[Tide]

Isn't a system anything you define it to be? So if I did define the system the way I did, then the external force acting on the car would be the normal force from the earth?

Yes, a system is anything you want it to be ... BUT ... you specified a closed system which means it's not interacting with anything else. The car is interacting with the Earth and so the Earth must be included as part of your CLOSED system.

 

[whozum]

Yes, a system is anything you want it to be ... BUT ... you specified a closed system which means it's not interacting with anything else. The car is interacting with the Earth and so the Earth must be included as part of your CLOSED system.

Then along those lines isn't the only closed system the entire universe? So other closed systems that are mentioned are usually for ideal purposes or mental exercises/

 

[Tide]

That's a dubious conclusion. Your example was blatant in that you had to apply a force to achieve a particular result and neglected an integral component in the force balance. Had you set up your car in a weightless environment (with adequate heating and air supply, of course!) you could have regarded that as a closed system -- and clearly seen that the act of raising your finger caused the car to move oppositely with the center of mass remaining stationary.

Clearly, closed systems can be defined for many situations and when something appears to "violate" basic physics that should be a clue you need to reassess your particular definition of "closed system."

 

[whozum]

Had you set up your car in a weightless environment (with adequate heating and air supply, of course!) you could have regarded that as a closed system -- and clearly seen that the act of raising your finger caused the car to move oppositely with the center of mass remaining stationary.

This is something I was going to ask about but I understood clearly in my head, however it raises the issue which goes along with your other statements: moving my finger would move the car, and since it was a force, wouldn't the me-car system will have a final velocity different to the initial velocity?

I lost my train of thought..