In this post, I am going to talk about real and not real forces as well as the fake centrifugal force (if you don't like the word "fake" you could replace that with "fictitious")
First, an example: suppose you are in a car at rest and press the gas pedal all the way down causing the car to accelerate. What does this feel like? If I weren't skilled in the art of physics, I might draw a diagram something like this:
Yes, maybe someone would add gravity and the chair pushing up, but this shows the important points. What is this force of acceleration? What causes this? This is EXACTLY the same thing as centrifugal force. If you think centrifugal force is real, this also should be real. I think this is enough discussion to show that this force (and centrifugal) is not real, but I will continue. There is another mystery: why does it feel like there is a force pushing you back when you accelerate? (if you have read all my blog posts, you may have a hint to the answer).
Let me replace the person with a model of a person. Here is my model (very simplistic)
In this model of a person, there are 4 masses each connect to the adjacent "atoms" with a spring (I represent the springs as rectangles because of my laziness). Now suppose I push on this model from both sides with equal forces.
I put these big bars on the side to make it clear the force was applied to both "atoms" on that side. So, when these two forces are applied, 1) the object stays at rest and 2) the horizontal springs are compressed.
Now what if I just apply 1 of these forces:
Notice that the compression is EXACTLY the same before (Eye-dentical). Hey wait! How do I know that this one force would compress this exactly the same? Well, you or I could easily model this and in fact I have done so for a [previous article (weightlessness and gravity)](http://scienceblogs.com/dotphysics/2008/09/gravity-weightlessness-and-a…)
If the above model looks the same, it means a person would feel the same. The only difference is that this person would be accelerating. The point of this story is that when a person accelerates, it FEELS like a force is pushing on you in the opposite way. One note: when you accelerate, it doesn't feel exactly the same as if someone was pushing on you. When someone pushes on you, they are exerting a force on just part of you. When you accelerate, it feels like something is pulling on ALL of you.
Ok, now on to circular motion and centrifugal force. In the above case, what if I took a "picture" of the velocity vector after 1 second? The two vectors would look like this:
And using the definition of acceleration:
I can find the direction of the acceleration by finding the change in the two velocity vectors:
Ok, so maybe we are all happy with this? (I am happy) Let me move to circular motion. I will once again "take a picture" of the velocity vectors for an object moving in a circle.
Now, I can do the same thing as before to find the direction of the acceleration. (it is ok to move a vector as long as you don't change its direction or length)
Key points: 1) the velocity did change (although only in direction and not in magnitude). 2) This change in velocity means the object accelerated. 3) in this case, the acceleration is towards the center of the circle.
This would make it "feel" like a force is pushing outwards. It is this force that people call centrifugal force.
Whenever one is thinking about forces, it is important to realize that forces are an interaction between two objects and there are only a few real forces. They are:
- Gravity - an interaction between objects with mass
- Electromagnetic - an interaction between objects with electrical charge
- Strong nuclear - an interaction between hadrons (protons and neutrons are two examples of hadrons)
- Weak nuclear - an interaction between quarks and leptons
Anything that is a real force should be one of these. Gravity is an easy one to pick out. What about me pushing on a book? That would be the electromagnetic force because the atoms in my hand are interacting with the atoms in the book (and that is what prevents my hand from going through the book).
What about centrifugal force? What are the objects that are interacting? (hmmmm.....) Which of the fundamental forces is it? (hmmmm.....). Well, it must not be a real force.
Don't get me wrong, sometimes the idea of a centrifugal force is useful, but that does not make it real.
In your models, assuming that the four masses are equal, the springs will compress half as much in the second case as in your first case.
To correctly model the fictitious force of acceleration, it must act on each mass in an amount proportional to that mass -- in your case, if the blue "seat force" is F, then the red "fictitious acceleration force" will be F/4 on each mass to balance the "seat force" and keep things static. Then the force compressing each of the two horizontal springs will be F/4, rather than F/2 as it would be if you model the force as just pushing on the left-hand masses...
True, that is why I put that big "plate" on the side so that I could push with just one force.
Great post! The thought experiment with the springs was a really nice way of looking at the problem.
I wanted to point out that in addition to these 4 forces, there is also the degeneracy force that you get when you try to squeeze a bunch of identical fermions together. It's different from the other four forces in that it's doesn't have any particle to mediate it - it's purely a quantum effect. But it's still quite real.
It would be interesting to try and figure out how much of matter not collapsing is due to electromagnetic repulsion and how much is due to degeneracy pressure.
This is incorrect.
When you exert a force to one end of the system with spring and masses (so it's accelerating) the compression is NOT the same as if you exert the same force to both ends of the system.
You should make a correct free body diagram to notice this.