Lever balancing physics (video game design)

[Fury22]

TL;DR Summary

Will the lever balance when two equal forces are applied to it?

Hi everyone! I am not a physicist or a physics student. Just a simple video game programmer. I have recently gotten into a discussion with my fellow programmer about a specific hypothetical problem regarding levers. The problem might seem very simple at first, but cause me a bit of headache.

So, let's say we have a lever with support exactly in the middle of it, so both sides arms are exactly the same length.
I apply exactly the same forces at both ends of the lever. Let's say 100 Newtons, or a 100kg objects. The amount of force doesn't matter. What matters is that the arm and the force is exactly the same at both ends.
However the lever initially is tilted all the way to the left side. So we locked the mechanism then placed the weight/force at both ends, and then we release the mechanism.

What happens? Will the lever balance out and rotate, so that it's completely flat? Or will it just stay still the same way when it was released?
If you know the answer, I'd like to know why you think this way.

My opinion:
In my opinion the lever will stay still, because the force on both sides results in equal, but opposite torque. But I might be wrong.

My friend's opinion:
My friend says it will balance itself. If this is true, I am curious what causes a 100kg object on the left to be lifted off the ground by the 100kg object on the right?

Thanks for any answers in advance!

 

[kuruman]

Newton's first law says "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." In this case, the forces are balanced, so guess what? You are right and your friend is not.

 

[Drakkith]

The lever should stay still since there is no net force, and thus no net torque.

 

[Lnewqban]

Welcome, @Fury22 !
It is important to consider the location of the center of mass of the system respect to the pivot axis.
Your friend believe is probably based on the way a simple balance works: naturally positioning the bar horizontally when both plates hold identical weights.

 

[Fury22]

Hi! Thanks for so quick and amazing answers!
Yes, so my friend's main justification for his way of thinking is the mechanical scales. He says that mechanical scales work in exactly the same way as my example, and therefore he can't be wrong. He also said that the location of the masses in relation to the pivot don't matter, which I disagree with.

So on this picture, it would level up like a mechanical scale, as you mentioned in the post above:

However, what would happen if the mass is above the lever? Let's assume this situation, let's say that the mass is attached completely stiff, on some hard metal bars or something. Would it also level itself?

 

[Fury22]

His explanation for the always balancing weight and weight balancing when over the lever was that these scales wouldn't work otherwise:

I am not an expert, but I think these scales work in exactly the same way, they just shift location where each of the weights are applied toward the bottom of the scale, which is hidden inside, but the actual centre of mass is still below the lever.

 

[Lnewqban]

However, what would happen if the mass is above the lever? Let's assume this situation, let's say that the mass is attached completely stiff, on some hard metal bars or something. Would it also level itself?
View attachment 338533

Your assumed situation (if you manage to keep each bar-weight perfectly vertical) would be a neutral balance: it should remain in the position your hands let it go.

Note how a real-world situation is a non-stable balance, as the left side lever (and its moment) grows as the system tilts counter-clockwise.

 

[Fury22]

Yeah, we assume the "perfect" scenario of course. In your example it would still stay to the left, because the arm on the left is longer, so more force is on the left.

 

[A.T.]

The lever should stay still since there is no net force, and thus no net torque.

No net force doesn't imply no net torque, so I would skip the "thus" here.

 

[A.T.]

He says that mechanical scales work in exactly the same way as my example, and therefore he can't be wrong. He also said that the location of the masses in relation to the pivot don't matter, which I disagree with.

The video below addresses exactly the misconception he has:

 

[Fury22]

Great video. It would be awesome to see similar one, but if the weights are not below the lever, but actually above.

 

[A.T.]

Great video. It would be awesome to see similar one, but if the weights are not below the lever, but actually above.

If the center of mass is above the pivot, it is unstable and any deviation from horizontal will increase.

 

[Fury22]

What if it's exactly at the pivot?

 

[A.T.]

What if it's exactly at the pivot?

If the center of mass is at the pivot, then it's neutral, so a deviation from horizontal will neither decrease nor increase, just stay as it is.

 

[Lnewqban]

Yeah, we assume the "perfect" scenario of course. In your example it would still stay to the left, because the arm on the left is longer, so more force is on the left. the net moment is CCW.

The net moment is the addition of the CW (right force x right lever) and CCW (left force x left lever) moments.
Note that what I call lever is always the perpendicular distance between the line of action of the force and the pivot.
That is the only thing that the geometry of each assembly makes change while tilting (except in the case of neutral balance).

 

[Drakkith]

No net force doesn't imply no net torque, so I would skip the "thus" here.

How so?

 

[A.T.]

How so?

https://en.wikipedia.org/wiki/Couple_(mechanics)

 

[Drakkith]

https://en.wikipedia.org/wiki/Couple_(mechanics)

Ah, I see.

 

[Fury22]

The net moment is the addition of the CW (right force x right lever) and CCW (left force x left lever) moments.
Note that what I call lever is always the perpendicular distance between the line of action of the force and the pivot.
That is the only thing that the geometry of each assembly makes change while tilting (except in the case of neutral balance).

View attachment 338574View attachment 338575View attachment 338576

Wow! This show the problem very, very clearly! Thanks for that explanation!