# What would be the direction of force exerted on two stationary posts by pivoting levers which are spring loaded? [closed]

I am having a difficult time with visualizing/determining what would be the direction of force exerted on two stationary metal rods by two pivoting levers which are spring-loaded.

To help explain what I am referring to, please consider the following drawing:

This drawing is showing a wooden board with two metal rods fastened to it (shown as blue dots), two rectangular metal levers with holes in them, so they can pivot around the metal rods, and a bungee cord (instead of a spring) that is fastened to each of the metal levers. Also, both of the metal rods are greased so the metal levers will easily rotate around them.

If you were to factor out air resistance and gravity such that this board was floating in interstellar space, when the two metal levers are pulled away from each other until they each reach a $$90$$ degree position from their at-rest position and are then released, as they are being returned to their at-rest position via the action of the bungee cord, will the direction of force exerted upon the two metal rods by the two metal levers always be towards point A?

Or, as the levers pivot around the rods, will there be some exerted force directed towards A, and some exerted force directed downwards towards the bottom of board?

I believe that the answer is that as the metal levers and the bungee cord accelerate towards their at-rest position, this will cause the metal levers to be pulled downwards due to the creation of centrifugal force (CF). So, as the levers rotate around the rods, the combination of the force being exerted towards 'point A' along with the centrifugal force pulling on each lever should result in a net direction of force that is in a slightly downward direction towards the bottom of the board. See revised drawing below. Unfortunately, I cannot prove this with formulas/equations for I have forgotten most of what I learned in a calculus course which I took back in high school, which was a long time ago.

## closed as off-topic by Aaron Stevens, Thomas Fritsch, Kyle Kanos, Jon Custer, ZeroTheHeroJul 5 at 20:19

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Aaron Stevens, Thomas Fritsch, Kyle Kanos, Jon Custer, ZeroTheHero
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• What have you attempted so far with this problem? – Aaron Stevens Jul 1 at 3:51
• I had made an answer, but then realized it might be taken to be a solution to a homework-like problem. This is why it would be best for you to say what you think, and to make the question more about the physics concepts you don't understand rather than just "what is the answer?" – Aaron Stevens Jul 1 at 3:58
• @Aaron Stevens, this is not a homework question, just something I have asked out of scientific curiosity. Also, I have added text in the description which may change the answer you had come up with. – HRIATEXP Jul 1 at 10:42
• Please read the description of the homework-and-exercise tag. It is not only for assigned homework problems. You should add to your question what you think the answer is. – Aaron Stevens Jul 1 at 11:46
• I have undeleted my answer – Aaron Stevens Jul 2 at 0:40

## 1 Answer

You are correct in thinking about the forces needed to cause the object to move rotate about the rod.

For rigid bodies of mass $$M$$, the center of mass will move according to $$\mathbf F=Ma_{com}$$ where $$a_{com}$$ is the acceleration of the center of mass.

Since the center of mass of each lever will move in a circle about the rod, there must be acceleration towards the rod. However, the bungee cord, if it remains horizontal, can only exert a horizontal force. Therefore, there must be vertical force components exerted by the rod while a lever moves.

So, if I were to correct your second diagram, it is that really there shouldn't be a centrifugal force (if you are watching this all happen from above in an inertial frame). However, there will be a centripetal force, which consists of the combination of the force supplied by the bungee cord as well as from the rod.