Swinging pendulum that swings forever?

[matttan]

Hi,

I know that when we swing a pendulum, it will stop a while later due to air resistance.

So my qs is if we are to put the same pendulum in a vacuum box, and only swing it only 1 time as before, will it ever stop or it will swing forever as there is no air-resistance?

Thanks

 

[Nick89]

There might be no air resistance in a ideal vacuum (although that does not exist), but there is still friction in the rotating mechanism, bearings etc.

If you could have a pendulum that swings forever, you could potentially harvest free energy from that (you only use a tiny bit of energy to get it going and then it keeps on going forever). This is called perpetual motion, and as far as the laws of physics as we know them tell us, it is impossible.

 

[Ranger Mike]

is it not true that Gravity is the limiting factor. it keeps limits the amount of swing..right?
the pendulum is pulling on the earth, the Earth is pulling on the pendulum and eventually the larger gravitational field wins out...or is this incorrect on my part?

 

[Vanadium 50]

If you could have a pendulum that swings forever, you could potentially harvest free energy from that (you only use a tiny bit of energy to get it going and then it keeps on going forever). This is called perpetual motion, and as far as the laws of physics as we know them tell us, it is impossible.

No, you couldn't harvest free energy from it. You could get exactly as much energy going out of it as you put into it, and not an erg more.

 

[Vanadium 50]

the pendulum is pulling on the earth, the Earth is pulling on the pendulum and eventually the larger gravitational field wins out...or is this incorrect on my part?

That's incorrect, I am afraid.

 

[matttan]

No, you couldn't harvest free energy from it. You could get exactly as much energy going out of it as you put into it, and not an erg more.

I know energy is neither created nor lost, but if we were to put it in a vacuum and take away the friction(ignore friction), then will it swing forever as potential energy converts to kinetic energy and vice versa forever or will the gravity cause the pendulum to stop moving?

 

[Doc Al]

I know energy is neither created nor lost, but if we were to put it in a vacuum and take away the friction(ignore friction), then will it swing forever as potential energy converts to kinetic energy and vice versa forever or will the gravity cause the pendulum to stop moving?

What stops the pendulum is energy "loss" due to air resistance and friction at the pivot, not gravity. Remove those losses and it will keep swinging.

 

[Dale]

If you had a pendulum in a perfect vacuum with a frictionless bearing and you started it swinging it would continue to swing indefinitely. However this is not what is meant by the term "perpetual motion" as it could not be used as a source of free energy. If you were to harvest energy from the pendulum you would have to exert a force on it which would slow it down. As Vanadium said, you would get out only what you put in and then it would stop swinging.

 

[Ranger Mike]

very enlightening..my education continues

 

[schroder]

Even if all air resistance can be removed, and the all friction removed from the top pivot point, the pendulum would still come to a stop. The reason is due to friction internal to the string itself. Each molecule of string (or wire or whatever is used) must exert force on the next molecule all along the length of the string. And all along the length of the string there exists friction losses which will eventually bring the swing to a halt.

 

[Doc Al]

Removing friction at the pivot includes removing internal friction at the pivot, where the string bends and flexes. The general tension along the length of the string would not count as friction.

On second thought, you may have a point. Since the tension in the string varies, it continually stretches and contracts, which would lead to energy losses.

Of course, in the idealized case, we ignore all of these complications. The main point is that it's frictional losses that cause the pendulum to come to rest, not gravity.

 

[Vanadium 50]

On second thought, you may have a point. Since the tension in the string varies, it continually stretches and contracts, which would lead to energy losses.

Only if you exceed the elastic limit of the arm. Otherwise it acts just as a spring, no?

 

[Doc Al]

Only if you exceed the elastic limit of the arm. Otherwise it acts just as a spring, no?

I would expect that any real spring has energy losses even within its elastic limit. (Or am I wrong?)

 

[Vanadium 50]

Couldn't we just be buy the perfectly elastic or rigid arm at the same place we bought the frictionless pivot?

To be honest, I am not sure. I never took strength of materials, just the prereq, solid state chemistry. What I know is that there are several different definitions of elastic limit, and the two that are most relevant are the "true elastic limit" and the "proportionality limit". The latter is substantially higher than the former, and below that point, even when you are moving crystal dislocations around in the sample, it still has a Hooke's Law behavior. That would suggest that if you were below the true elastic limit you'd be find, and above the proportionality limit you'd still probably be fine.

The reason I still have some doubts has to do with temperature. So long as the rod is not at absolute zero, eventually you will induce defects in the crystal, and eventually these defects will move under a combination of the forces induced and thermal effects. On the other hand, probably long before this point you have to worry about thermal effects on the bob itself, as it is absorbing and radiating photons all the time, gaining and losing energy as it does so.

Finally, quantum mechanics tells us the pendulum cannot stop. There will be a minimum energy of $$\hbar \omega / 2$$.

 

[Doc Al]

Couldn't we just be buy the perfectly elastic or rigid arm at the same place we bought the frictionless pivot?

I'm with you!

Though I also never studied strength of materials explicitly, the more I think about it the more I'm convinced that real, macroscopic springs must suffer some internal damping. But I suspect its small.

I've seen terms like "coefficient of energy dissipation" and "energy dissipated per cycle" describing internal friction in springs, but I don't really know anything about it.

We need a mechanical engineer!

 

[Mapes]

Perfect elasticity is a simplified model; all materials, even single crystals, permanently deform to some extent under load (i.e., they creep). The amount is negligible--but not absent--in metals at less than about half their absolute melting temperature. As Vanadium 50 alluded to, the mechanism is flow through vacancy diffusion, and vacancies always exist above absolute zero.

So a frictionless pivot and a vacuum wouldn't be enough to keep the pendulum from slowing down.