Puzzle 4

[zekeman]

Defyiing law of angular momentum?

Here is a fun puzzle for you purists.

How is it that a kid sitting on a swing starting at rest can, without any help, always cause the swing to oscillate?

Please explain.

 

[btrueblood]

"< why forget him. I was referring to him>"

Didn't say forget him, I said forget the section that discusses standing/sitting motions, as they point out that this motion will not start a swing from the rest position.

>A perfect pin has nothing to do with a rod that replaces an ideal rope>

Taken out of context, the following statement clarifies.

> why add a another complication to an already complicated system. And, moreover, by adding another link you are still left with the rope above his hand where I suppose you get another ideal pivot, but what is the point>

To model the physical reality.

"> Those are the strangest free body diagrams I have ever seen."

Thanks. Yours, of course, are invisible to me.

"I don't have a clue."

Given.

I'll admit the fbd's are less than complete, merely a method to try and describe the physics. Fig. 2b tries to describe the motion of the center of mass, ignoring any force input from the upper hinge (pure inertial reaction). The com must shift relative to the upper pivot for this case. Fig. 2c tries to describe the condition where the upper pivot must remain in-line with the center of mass as the rods change their angle relative to each other. The two cases are obviously different. I am trying to figure out why - but the realization that Fig. 2c only applies if the angle is changed very slowly, so that static equilibrium applies, and that fig 2b is the condition when the angle is changed very rapidly, makes me think twice. Like I said, I'd have to grind out the math to prove one way or the other.

> Look in your neighbor's backyard.You don't really think its a rod or it has weight significant enough to change a well developed model. The models that do not allow for a flexible rope are somewhat.>

My neighbor's swing has rods from two pivot points (glider swing). Are somewhat what? I dunno either.

"I now firmly believe that any method of increasing the energy of the system,standing or thrashing will increase the velocity at the 0 position and thus increase the amplitude. Absent friction it will runaway."

Ok, we disagree again I think - standing and sitting won't start a swing from the rest position, only the rocking motion will.

IDS: "Starting from rest you need to displace the rope horizontally at some point, and you can do that by pushing another part of the rope in the opposite direction. Once there is even a small deviation from the vertical you have a source of a horizontal reaction, and can start to move your centre of mass in the horizontal direction."

Yup. It's that first displacement that has me wondering again, but I'm satisfied with that statement if you are.

Good night.

 

[zekeman]

IDS,TB--easpecially IDS
If you bothered to read my posts, I have repeatedly said that it is impossible to start a system at the rest position (assuming no air ) since you cannot generate an external horizontal force
My take on standing and thrashing assumes the motion has started.
So, since we are almost all in agreement about the starting problem,I guess we can put this to bed or have another marathon on ropes and models and math solutions.
But, I will now stand ( no pun intended)_on the standing/sitting and pumping means of making the amplitude grow until friction will limit it, with or without an ideal rope.

 

[FeX32]

This thread is oscillating.


Fe

 

[GregLocock]

Looks more like chaotic motion to me.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[FeX32]

Haha! you're right



Fe

 

[handleman]

Does anyone disagree that leaning back and kicking your legs forward results in a net rotation of mass?

Does anyone disagree that it is possible for a kid to do this on a swing that is hanging purely vertical?

Did someone say something about conservation of angular momentum?

-handleman, CSWP (The new, easy test)

 

[jistre]

I so want to contribute to this thread. I so don't want to read through the whole thing to make sure my point hasn't already been made.

This thread makes my head hurt.

 

[FeX32]

As before, it's time for a:



Fe

 

[rb1957]

"Looks more like chaotic motion to me" ...
nah greg, simple harmonic ...

 

[FeX32]

... if you look at it that way, it definitely is at the natural frequency by now


Fe

 

[btrueblood]

I still like Greg's paper. The gal in Fig. 1 is a swinger, I'd sure like to meet her.

 

[btrueblood]

I'd like to know if anybody has access to AJP archives, and can download the #4 reference from my 1st listed paper, "On the starting of swings at rest" by McMullan? Wondering if there is any detail there...

 

[FeX32]

yea, wonder what her "frequency of oscillation" is.


Fe

 

[btrueblood]

Or her frequency of osculation...

 

[Compositepro]

I don't know what the right answer is and with many of the posts I'm not sure which position is being supported.

Let's consider another example. The Rings in men's gymnastics is a swing and maybe easier for visualization and degrees of movement of the person. Now clearly there are lots of movements and rotations that will not produce produce swinging, as that is the point of the sport. However, the "swinger" (lots of google hits, btw) can perform a kip where, while hanging by his arms, he brings his legs over his head with is body folded at the hips. He then trusts his legs in a direction that is 45 degrees up from horizontal. In free-space this would of-course have no effect on his center of mass, but he is on a swing. The rings swing one way and the tension on the rope increases over the weight of the swinger. So during the leg acceleration there is a horizontal component of force on the center of mass (COM). When the kip is finished and the legs are decelerating, the rings will be on the other side of vertical from rope pivot point, along with the center of mass, which has been slightly displaced. During deceleration of the legs the rope tension is again higher than the swingers weight and there is a horizontal component of force applied to the COM which adds more energy to the swinger.

I vaguely remember doing this as kid. I guess that angular momentum is involved here but is not need for explanation (and would probably just confound understanding). It seems that the key is finding a way to create a small horizontal impulse to the swing that is not canceled by an equal and opposite reaction. The technique I described assures that the equal and opposite horizontal reactions naturally occur on opposite sides of vertical. So, it appears that it is possible to start a motionless swing.

Now I need to think if something similar is possible while seated.

 

[ivymike]

it's obvious that you can create a torque on an object at the bottom of a "perfect" string using the string (and gravity) alone... if someone is objecting to that, picture a winch on the bumper of a jeep, reeling itself up a cable. It should be apparent that such a maneuver could be made to work without the help of friction.


Here's an idea, based on the rocket... perhaps you can model this one, Greg. Picture a guy at the bottom of a perfect rope. Anytime he sticks his legs out, the rest of him goes the other way to keep the cg perfectly below the pivot. This guy is a clever fellow, though, and has someplace to be in the afternoon. He unravels his shirt into a long thread, ties it to his wallet, and throws the wallet as far as he can. This little push gets him off of dead center and starts him oscillating, at which point he can "pump" conventionally to build momentum. He has a really good arm, so he builds momentum While the wallet is still airborne. Eventually it comes to the end of the thread and stops, and he reels it back in before it ever hits the ground. He gets to keep a whole lot of momentum.

Maybe rigid bodies behave much differently than very flexible (or separable) ones?

 

[FeX32]

take a rope. put an inertial actuator on the end.
Or just a motor and a disc with a hole in it. Can it start oscillation of the rope.....

p.s. tune the frequency of the actuator to "her frequency of osculation".


Fe