# Balance, pendulum and energy

• cala
In summary, the conversation discusses a video of a pendulum attached to a balance arm and the concept of extracting more energy from the balance movement than is needed to keep the pendulum swinging. The conversation also includes calculations and explanations of the forces involved and the inefficiencies of the apparatus. The conclusion is that there is no extra energy being generated and the system is simply experiencing losses due to friction and impact.
cala
Hi. I saw this video on google:

It's mainly a pendulum attached to a balance arm.

It's stated that the energy needed to keep the pendulum going is far less than the energy we can extract from the balance movement.

I also post some pictures to try to show how it 's supposed to work.

This is how i suppose it works:

The force of gravity on the pendulum de-composes into two components as it oscillates: one is tangential acceleration, that keeps the oscillation going and the other one is a perpendicular force to the pendulum "track".

When the pendulum is in vertical position, tangential force is 0, and perpendicular force is at maximum value. When the pendulum is at the 2 top points of its path, the tangential force is at maximum value, and the perpendicular one is at the minimum.

The perpendicular force doesn't affects the pendulum's oscillations. Only the tangential component maintains the pendulum oscillating. Usually, the perpendicular force is compensated with an opposite force on the "strongpoint" of the pendulum... But what happens if we put the "strongpoint" of the pendulum pending from an arm of a balance? It's exactly the same as if we put a "variable weight" on this side of the balance, so the other side of the balance (if it has a fixed weight) will move up and down, just as if we put more or less weight on the side of the pendulum.

So the question is: Why it's needed more energy to keep the pendulum oscillating than the work we can extract from the movement of the balance by the "variable weight" that is on the pendulum's side of the balance?

The variation of the perpendicular component of the pendulum's weight is just a consequence of the pendulum oscillation, and usually, it's not used to do anything. But this perpendicular component can take values from 100% to 10% of the total weight of the pendulum while the pendulum is oscillating. So why the input work (for maintain the oscillation) should be equal or higher than the work we can extract from the balance movement by using the "variable weight" of the perpendicular force?

Do you know an expresion that relates the loses on the pendulum's oscillation and the work on the balance?

Can you explain why the work the perpendicular component can do have to be less than the loses we have to restore on the pendulum's oscillation?

Thank you.

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I think it is a hoax. The motions of the swinging weight are not driving the system, there is something hidden doing the work.

I don't think it's a hoax, just someone has misinterpreted what's happening and assumed that the hammer end must be using more energy than what is supplied at the pendulum.

Ceisumfrog is right - it isn't a hoax, it is just a misunderstanding of high school physics.

A little more explanation:

I admit I only got about 5 minutes through a 35 minute video, but unless it got a lot better, the issue is relatively clear. The guy didn't do any calculations or take any measurements, so what he has is his intuition that there is more energy expended in raising and "dropping" a weight than is lost in the pendulum. But *my* intuition (which doesn't contradict the first law of thermodynamics, btw...) tells me that there is very little energy expended in raising and lowering a weight by moving a pendulum.

Thank you for taking time to analyze the system.

Lets put some numbers, and maybe you can help me:

Imagine the pendulum has a mass of 10Kg, with a length of 50cm, and the balance is 1m of length and has a fixed mass of 10 Kg at the other end of the balance.

Imagine we manage to get an angle of oscillation of 60º...

-How can I calculate the energy input (in an easy way) to maintain the oscillation angle of this pendulum on 60º?

-What is the perpendicular force value on the "strongpoint" at the ends of the path and in vertical position?

-How can i calculate how much work can be done using the movement of the balance caused by the pendulum "variable weight" on the other end? (Or maybe, what is the height difference on initial and final position, to get the potential energy difference...)

If you can give me no simple equations or numbers, please try to explain the process, and why the work to keep the oscillations going should be higher than the work we can get from the balance movement.

I don't understand your first question: a pendulum requires no input energy to keep moving after it is started. That's the whole point of a pendulum!

For the second, the forces at the sides are found via trigonometry (draw a free-body diagram with the weight and angle) as the speed is zero, so there is no centripedal acceleration. At the bottom, it is the weight plus centrifugal force.

For your third, the whole point here is that you can't calculate the work done because there isn't any in an ideal case! All of the energy lost at the weight on the other end is due to the impact and friction in the apparatus. It is heat and sound. There is no height difference because the weight starts and ends at the same place. When the weight is lifted, it takes kinetic energy from the pendulum and converts it to potential energy. When the weight is lowered, it gives that potential energy back and the kinetic energy of the pendulum is restored. It would be easy to see if you played with the device (and maybe he showed this...), that very small adjustments in the height the weight would be lifted (thus, very small change in the potential energy when it is lifted) would result in large changes in loss and thus large changes in how long the pendulum would swing. That's all just inefficiency.

A better apparatus to demonstrate this would have a spring connecting the weight to the platform instead of having it rest on the platform. Such a device would show clearly the conservation of energy and would oscillate for a very, very long time.

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I was about to put that theoretically a pendulum needed no energy to input when I saw your answer.

So the loses we have to restore are just friction ones (low energy indeed!).

But i don't agree with you on the part of the balance. I mean:

The perpendicular force of the pendulum acts like a "variable weight" on this side, that is like a "variable mass"...

So when the weight goes increasing, gravity is doing work pulling this side of the balance down, and this work is compensed on the other side of the balance, rising the fixed weight.

When the "variable weight" of the pendulum goes decreasing, then the gravity does the work on the fixed weight part (that goes down), and then this work is compensed on the side of the pendulum, rising the whole arm, and gaining potential energy...

If you do the complete account of energy for the whole balance, it is clear there are no gain on energy, but if you look only on the fixed weight part, there is always something doing work!

When the fixed weight go down, gravityt is doing work, and when the fixed weight goes up is just because something on the other side of the balance is doing work (the "variable mass" and gravity on the other side... again!)

If you can do work with a balance in which you put and removes weights on one side, then this device should work as stated.

cala said:
If you do the complete account of energy for the whole balance, it is clear there are no gain on energy, but if you look only on the fixed weight part, there is always something doing work!
The accounting of the fixed part looks like this:

x+(-x)=0

When the weight is lifted, it takes energy, when the weight is lowered, it gives it back.
When the fixed weight go down, gravityt is doing work, and when the fixed weight goes up is just because something on the other side of the balance is doing work (the "variable mass" and gravity on the other side... again!)
Your statements are incomplete/inaccurate and should read:

"When the fixed weight goes down, gravity is doing the work"...on the weight, against the combined forces on the pendulum.
"When the fixed weight goes up [the combined forces on the pendulum]"... are doing work on the weight, against gravity.

As you can see, the two statements are mirror images of each other, hence "X" and "-X".

Somehow you see gravity doing work on both sides and don't see that that makes it symmetrical. But if you just have a pendulum, you can easily see that gravity does all the work there and the work is symmetrical, can't you? This is only very slightly more complicated.
If you can do work with a balance in which you put and removes weights on one side, then this device should work as stated.
I'm not exactly sure what you mean there, but if you remove weights while the system is operating, then you are doing the work to keep it operating.

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When i say "if you put weight, and then removes it in one side of a balance, you can extract work on the other side of the balance." then you say "you are doing the work"... and that is exactly what the pendulum oscillation is doing for free! (because the change on the perpendicular component is for free, no energy consuming)

I mean: Imagine a balance with a weight on one side.

Now, you put some weight on the other side, the balance rises, you put more weight, the balance keeps moving...

Now you remove some weight, the balance goes down, you remove more weight, the balance keeps moving on same direction...

Is there no work being done on the inital weight of the other side?

I think the answer is yes, there is.

The pendulum is just equivalent to put or remove weight on one side of the balance... but for free!

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cala said:
When i say "if you put weight, and then removes it in one side of a balance, you can extract work on the other side of the balance." then you say "you are doing the work"... and that is exactly what the pendulum oscillation is doing for free! (because the change on the perpendicular component is for free, no energy consuming)
No, it isn't. The key word here is extract. You cannot extract energy from this system or it will stop moving.

I'm not going to pursue this line of thinking because if you can't understand the original scenario, changing it is just going to confuse you more. This is a big red-flag of crackpot logic (as is the "convince me I'm wrong" mindset: no -instead, keep your mind open and make an effort to learn). Heck, the original scenario is two simple concepts put together in a way that only increase the complexity a little bit and you can't even grasp that!

I don't know how to convince you of this and I'm not inclined to waste much more of my time trying to teach someone who doesn't want to learn. You're going to wast a lot of time and effort chasing somthing that doesn't exist if you insist on keeping your blinders on here. People have wasted their lives in search of perpetual motion. Don't waste yours. Make an effort and learn some real physics.

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I'm sorry, but still don't know what is the answer to the question:
Changes on a variable weight on a balance can do work on the other side of the balance?

ask yourself, what is happening on the pendullum side.
KE is being turned into PE and the pe reaches a maximum value when the KE equals zero at the top of the oscillation.

this PE would then be equal to mg delta h which would also equal the total energy of the system.

if you extract energy from this system the maximum height that the pendullum would reach changes. Thus on the next cycle there is less energy to extract from the system, you can continue this until the pendullum stops moving (as there would be zero energy in the system).

the uy in the video also periodically pushes on the balance in order to maintain the oscillation (thus adding energy)

and he seems to think he has a new way of amplifying mechanical force, when in reality he's dealing with a lever of sorts and an oscillation.
9

Thank Luke, good analisys.

But why the movement of the balance should quit energy to the pendulum?

Imagine that the pendulum is not connected to the balance. It transforms KE to PE, and it gets a potential energy with a height of "h".

OK. Now, connect this pendulum to the balance. We should get the same "h" difference from oscillation, plus more height, due to the work the balance (from gravity) do on the fixed weight part. If you "extract" this work, then the fixed weight will do not rise the balance on the pendulum side, but the initial "h" of the pendulum maintains in the same value. So we have the same "h" always, and more or less height due to the balance movement. This aditional height is a consequence of the oscillation, but does not affect the oscillation.

That is why it's stated that the balance doesn't affect the pendulum.

Don't you think so? Is there some error?

honestly, please stop analyzing physics using words. Learn how to describe a physical system qualitatively. Either draw a free body digram, work out the forces, or get a Lagrangian.

descriptive physics gets you nowhere.

tim lou is absolutely correct, this problem would easily be resolved for you if you worked out the forces.

however in response to your previous question, the balance is set up such that when it raises the pendullum (when the system is at rest) in a way such that the pendullum rises perpendicularly, this stores energy in the form of gravitational potential. When the balnce lowers the energy is returned in te form of kinetic enery. This kind of motion will result in no net increase of energy in the oscillator.furthermore even in the case when the pendullum wasn't at rest andsomeone did work on the beam, it only raises the pendullum a tiny amount, adding very little energy to the system, whereas by moving the pendullum you are free to add a lot more eergy to the system.the entire system works like a lever really

also a mathematial analysis yields

-mgh +mgr cos theta

where h is the height difference between that the lever arm oscillates through, as the total energy of the system when the pendullum is at the botom of its swingthat mgh term is the energy gotten from the pendullum going dropping down through the lever height, and the mgrcos theta is the energy gotten from swinging from its intital height, (note this assumes that both parts of the system are set up such that the lever reaches its maximum height when the pendullum is at the bottom of its swingnow let's say that on every oscillation the lever sucks out an amount of energy equal to E0, then the next oscillation would have a total energy equal to

E-E0=mgh-E0+mgrcos theta=mgh1+mgrcos theta1

and I'm sure there's another equation lurking somwhere that will allow you to solve that equation, however you can see that h and theta will both decrease, and this will continue until they are 0.
which for some reason unbeknownst to me always yields E0 equals zero, I haven't had a full intermediate mechanics course so maybe someone could point out the error here for me.

I've seen the video and:
1) the system needs energy. Only one finger can do the job, but needs energy supply.
2) The pendulum is heavy and attached to the short arm. So an small movement on the short arm wil be greater on the other side. This is not magic. But is more common to use in the other way: wide and weak movement produces a short and powerful one.
3) Gravity is working all the time on both parts. You should not use gravity where you like.

You could obtain a 25Kg hammer activated by a finger hanging it from a spring.
The device performs an interesting hammering in an easy and convenient way, but again, it's not magical, it is not a continuous movement machine.

It's not stated as a perpetual motion machine,

It is suposed to give more output than input.

I think the correct answer is NO... but the video seems to show the machine working that way...

cala said:
It's not stated as a perpetual motion machine,

It is suposed to give more output than input.
That is the definition of a perpetual motion machine (type 1):
A perpetual motion machine of the first kind produces strictly more energy than it uses, thus violating the law of conservation of energy.
http://en.wikipedia.org/wiki/Perpetual_motion
I think the correct answer is NO... but the video seems to show the machine working that way...
No, the video clearly shows the man adding energy to the system by pushing the pendulum. It most certainly does not "seem" to work.

In your previous post, you indicate a belief that the energy of the pendulum is independent of the up and down movement of the weight on the other end, yet at the same time acknowledge that it is the pendulum that is moving the weight. CPL.Luke is right that you should draw a fbd, but that's a logical oxymoron anyway. You can't believe both things at the same time.

The paradox stated by the man in the video is that the system is moving a 25Kg hammer and you *only* need to put an small amount of energy using a single finger.
Imagine a kid swinging: he can achieve wide oscillations just moving slightly his legs back and forward at each cycle.

It's not an small amount of energy the one you can add at each cycle with a single finger. It is just that the hammer movement seems so powerful (something the man itself is trying to show), and this is due to the amplifying efect of the longer hammer arm. But with the finger you do not add the energy to move it, just the one you are loosing at each cycle, as the whole movement is oscillatory.

Exactly, vivesdn. The guy in the video is missing the fact that there is very little energy loss at the hammer. Lifting it up and lowering it back down is a conservation of energy process and he doesn't realize that because he thinks the hammer is being dropped (his word). He thinks work is being put into it by the pendulum but doesn't understand that the hammer then puts the same energy back into the pendulum, minus the loss of his (self-admitted) poorly constructed device.

I toured an old paper mill recently where a water wheel with a ratchet lifted and then actually did drop a hammer (to pound paper flat). If you attached such a ratchet to this device in order to make the hammer drop freely instead of lowering it, you'd find the pendulum quickly stops, just like a kid on a swing stops himself by adjusting the phase of his swinging legs (I was actually thinking about that example a few minutes ago...).

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The reason things like this irritate me so much is that though the concept is relatively straightforward, the scientific analysis and testing of the device is excruciatingly simple. This guy went to enormous lengths to build a device and make a video when actually measuring what the device is doing is kiddie-play.

When I was in high school, we analyzed simple harmonic motion with stop watches, a ruler, and a projector. You can easily test the conservation of energy by measuring exactly how far up and down each piece moves, applying the simplest energy equation ever (e=mgh) and comparing the numbers. I'm not sure what he thinks the platform is doing, but the device is inherrently stable, so you can simply remove the platform and watch how the energy is conserved.

If you want to anayze it in terms of forces, it is much more complex, but quite frankly, that's only necessary if you take the starting position of tossing conservation of energy in the trash, and that's just idiotic. So computing the energy by analyzing the forces and motion isn't really necessary. Perhaps that lends credence to Integral's hoax theory - in order for this guy to be for real, he has to be wearing blinders, assuming from the start that perpetual motion is real. If he's not pulling our leg, he's got to be spectacularly dense.

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## 1. What is balance and how is it related to pendulums?

Balance refers to the state of equilibrium or stability of an object. In the context of pendulums, balance is important because it allows the pendulum to swing back and forth smoothly without any external forces disrupting its motion. This is crucial for accurately measuring time using pendulums.

## 2. How does a pendulum work?

A pendulum works by converting potential energy into kinetic energy and back again. When the pendulum is at its highest point, it has maximum potential energy. As it swings down, this potential energy is converted into kinetic energy, causing the pendulum to gain speed. As it reaches the bottom of its swing, all of its potential energy has been converted into kinetic energy. The pendulum then swings back up, converting the kinetic energy back into potential energy.

## 3. What factors affect the period of a pendulum?

The period of a pendulum is affected by three main factors: the length of the pendulum, the mass of the pendulum bob, and the acceleration due to gravity. The longer the pendulum, the longer its period will be. The heavier the pendulum bob, the shorter its period will be. The stronger the force of gravity, the shorter the period will be.

## 4. How does energy play a role in the movement of a pendulum?

Energy is essential for the movement of a pendulum. As mentioned before, a pendulum converts potential energy into kinetic energy and back again. This conversion of energy allows the pendulum to continue swinging without slowing down. The energy is conserved throughout the motion of the pendulum, meaning the total energy remains constant.

## 5. Can pendulums be used for anything other than measuring time?

Yes, pendulums have many practical applications. They are commonly used in clocks and metronomes to keep accurate time. They are also used in seismometers to measure the intensity of earthquakes. Pendulums are also used in amusement park rides, such as swings and pirate ships, to create a thrilling and oscillating motion. In addition, pendulums have been used in experiments to study gravity and the Earth's rotation.

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