One part of me says no, because the force of gravity would eventually drag it to a stop, but part of me says in an ideal setting, there would be perfect conservation of momentum and the pendulum would swing forever. Dopers? Some basic physics help, here, please. xo, C.
Gravity is a comnservative force. You gain back what you lose to gravity during the swingm, and vice versa. Gravity itself won’t stop your pendulum (the planets have been orbiting the sun under the force of gravity for billions of years now).
It’s NON-conservative forces that do you in. Like friction. Even in the absence of friction, you still have air resistance. Without friction or atmosphere, your pendulum will probably continue rocking for a very long time.
>Gravity is a comnservative force. You gain back what you lose to gravity during the swingm, and vice versa. Gravity itself won’t stop your pendulum (the planets have been orbiting the sun under the force of gravity for billions of years now).
Wrongo, Bucko. Gravity is conservative in one sense, but in another, it is an agency that carries, by radiation of gravity waves, energy out of the system. The planets have orbited the sun for billions of years, but not with all their original energy. Some of it has been radiated in gravity waves. I think the most energetic events known in the universe are galactic-size black hole mergers, which can convert on the order of a half a galaxy’s worth of mass directly into energy (multiply half a galaxy of mass by c^2!) and radiate it away.
How wrong do you wanna be? loss of energy by gravitational radiation, even by planet-sized masses, takes ca LOOOOONG time. Its effect on a pendulum of human dimensions is gonna be negligible compared to practically anything else. Electromagnetic effects on the damned pendulum will be more important.
Gravity does drag it to a stop – at the top of each swing.
In a Newtonian universe, the pendulum would swing forever. Those happy-go-lucky 17th century bastards didn’t have to worry about gravitational radiation.
“probably”? “a very long time”?
What about forever? That’s really my question.
If you’re going to take that long a view, then I doubt it will go forever. Moon rocks set into motion by a moonquake, even in the absence of air, will eventually stop rocking. Friction, which is uniquitous (and which you can’t, really, completely get rid of. It’s going to be your biggest headache in trying for perpetual motion). You’ll be pelted by microm,eteorites and particles from the solar wind. Cosmic rays will zap them and change charge states. Internal friction and metal fatigue will have effects. You’ll interact with electric fields and magnetic fields. Light pressure , if it’s from one side, will effect your swings. Eventually, any tiny effect will cause you problems. But the biggest single effect of all those effects, I predict, will be to cause more friction, which is the one effect you pretty much threw out the window at the start.
Are you counting hysteresis as friction?
Do you really mean, “In the abscence of friction”, or do you really mean, “In the abscence of any force that would make it stop”.
Because in the abscence of any force that would make it stop, the pendulum will go on forever. Our planet has orbited the sun for 4 billion years, and it will continue orbiting the sun for billions more.
It will eventually stop orbiting the sun, but only because outside factors will intervene. The sun will run out of nuclear fuel, balloon up to a red giant, and swallow the earth, and friction will stop the earth’s orbit.
If we could compress the sun into an object with the exact mass of the sun but wouldn’t change into a red giant, then the earth would continue orbiting for billions and billions of years more. But eventually, eventually, the orbit would stop, because of friction. Every micrometeorite, every cosmic ray slows the orbit of the earth by a microscopic increment. Add up trillions of such impacts over trillions of years, and eventually the orbit will decay, and the earth will eventually impact the sun, and the orbit will stop.
So if we stipulate that there are no forces to stop the pendulum, then the pendulum will indeed go on forever. But of course, there are always forces that will stop the pendulum, so it can’t go on forever.
I mean “in the absence of friction.” It would be clear to me that in the absence of any force that would cause it to stop it would continue. I’m really asking about the idea of conservation of momentum, I think, in the presence of gravity. I’m trying to confirm my understanding that gravity alone will not bring a pendulum to a stop. Unless, of course, it forces surfaces together and creates friction. But I’m trying to eliminate that in this scenario.
If you’re going to worry about the gravitational radiative losses, you also need to worry about the electro-magnetic radiative losses. All those moving charges produce radiation. If I had to hazard a guess, I would say the EM losses will be much greater than the G losses.
No, it’s conservation of energy that defines the motion of the pendulum. At the beginning, when you pull it back to release it, p* = 0. But you’ve stored potential energy in the system, which gets converted to kinetic energy and then back into potential energy again.
*p = momentum
OK.
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Forever is a very long time. If that’s what the OP wants to answer about, well, let’s answer about that.
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CalMeacham is very probably right that electromagnetic interactions would be much more important than my radiating gravity waves. Good point.
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“I’m trying to confirm my understanding that gravity alone will not bring a pendulum to a stop.” Well, if by “gravity” you strictly mean the attraction the pendulum bob feels downward, and want to look at it in a classical sense in which it is felt everywhere simultaneously and does not need to radiate, that would exclude gravity waves. If by “gravity” you mean the whole ball of wax, you’d have to include gravity waves too.
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The pendulum is hanging from some pivot that, I suppose, is coupled to the rest of the Earth. Unless you assume the mounting of the pivot to be perfectly rigid, the pendulum is also making the pivot move around a little. If you want, you can claim the pivot mount is perfectly elastic, in which case it does not consume energy to keep moving it around a little. If you want a pivot that is mounted using real materials, your pendulum will lose energy because moving the pivot mount around a little will dissipate energy due to the inelastic component of the pivot mounts. Some people call this friction, but it’s not the kind of friction you get between sliding surfaces on what we consider separate objects. It’s the kind that takes up your energy when you keep bending a wire back and forth as if to break it. You would have to decide whether to count this. Santo Rugger asks about hysteresis - hysteresis has many physical manifestations, but I guess this is the one he means. Note - this entire paragraph is referring to things OTHER THAN bearing friction in your pivot itself, which we already stipulate is zero.
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Momentum isn’t the important thing being conserved. In fact, if you are claiming a perfectly stationary pivot, then momentum is not being conserved. In a real pendulum, the pivot mount and the Earth it is connected to hold all the momentum between them, in the same quantity but opposite signs, that drops to zero at the ends of the swing.
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Baldwin’s right, of course, though that’s not the answer you were seeking.
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You’re conserving energy, like John Mace says.
That’s pretty similar to what I was alluding to. I was thinking of a mass at the end of a rod. At the end of every stroke, when the mass is stopped, the rod is going to flex, as it won’t be perfectly rigid. When it bends, the momentum is going to be converted to hysteresis, which will manifest as heat. I strongly suspect this will have a much greater effect on the system than any electromagnetic or gravity waves.
>I strongly suspect this will have a much greater effect on the system than any electromagnetic or gravity waves.
You may be right. I’m not sure whether electromagnetic or elastic losses would be worse. I think the gravity wave loss would very likely be much smaller than either, though.
We also didn’t consider the pendulum rod or thread (is this a rigid or flexible pendulum?) changing its length, but the tension on it is maximal at the bottom of the swing and minimal at the ends. There would also be hysteresis losses from this tension on the rod or thread if it’s made of real material.
Precision timekeeping was based on pendulums until the development of quartz crystals. A design called the Shortt Pendulum (Shortt was the name of the inventor) kept a pendulum in a vacuum and arranged another pendulum to be a slave to it. I think the Q on this was something like 10^5 or 10^6. IIRC, the amplitude of a pendulum swing goes down by e to the power -S/Q where S is the number of swings, so this pendulum would still be swinging with about a third of its original amplitude after 100,000 or 1,000,000 swings.
Honest question, would a pendulum swing with no friction? Is friction something that is needed for it to even move at all? 
I’m not phrasing it well I know, but I hope someone can see where I’m coming from/going with my musing here and give me an answer I can grasp.
I’ve definitely learned something about gravity - I was not aware of gravity radiation.
As an engineer, I liked the question about the materials. Beyond the hysteresis question, if the pendulum’s materials are real (except for the non-friction aspect), then the repeated alternating stresses will result in the pendulum failing due to fatigue at some point before “forever”. My guess is that would happen before it came to a halt due to the other factors.
It’s not right to assume that just because there is gravity there is gravitational radiation. For example I don’t think a massive object undergoing SHM produces gravitational waves in itself.
If I had to guess I’d say yes there probably is gravitational radiation as a high-order effect, but the actually effect would be almost incomphrehensively small.
The question is poorly defined. “Forever” for anything is impossible because earth (and the universe probably) will not last “forever.” A very very long time? Sure.
>It’s not right to assume that just because there is gravity there is gravitational radiation. For example I don’t think a massive object undergoing SHM produces gravitational waves in itself.
Well, of course it is. I mean, it isn’t an assumption. Any change in a gravitational field propagates away from the matter that is creating the change, at the velocity c. If it propagated at any other speed, then it would be possible to define a real physical reference frame in which the effect caused by the change in the matter preceeded the cause itself, which violates causality.
A massive object undergoing simple harmonic motion certainly changes the gravity field around it, including out to infinite distance, in this way. Even a massive object that is simply rotating in a sense in which it does not have rotational symmetry has to do this.