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.

 

[GregLocock]

Back to swingy things.

If I replace the torsional spring between the seat and the rigid chain, what difference will it make?

The system is now

earth
revolute joint
rigid masless link to replace chain
rotational bush
high inertia seat
motorised revolute joint
leg pendulum

with gravity as the other constraint.

Also, try and predict what will happen if i replace the rigid chain by 5 massless links.

One thing you might like to think about is a 2dof system that consists of earth/ spring/ mass /linear motor /small mass, and what that system does as a function of the linear motor's activities, both in theory and then in practice.





Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[ione]

IMO the point is changing the position of centre of mass of the whole system (swing + kid mass) with respect to the hinge so to let gravity play its role and accelerate the swing. Then the conservation of angular momentum will do the rest.

 

[SomptingGuy]

Which is kinda how I tried to describe it. Kids can shift their COG quicker than swings can restore it.

- Steve

 

[GregLocock]

So, is the problem that there is no problem?

Perhaps that is a better way to phrase it

Given a simple 2dof system, why would you expect to not be able to excite a resonant response, given control over one dof?





Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[IDS]

IMO the point is changing the position of centre of mass of the whole system (swing + kid mass) with respect to the hinge so to let gravity play its role and accelerate the swing. Then the conservation of angular momentum will do the rest.

How can you accellerate the centre of mass of the system (everything below the pivot) if there is nothing to provide a horizontal reaction?

Which is kinda how I tried to describe it. Kids can shift their COG quicker than swings can restore it.

Can they?

Where does the horizontal force come from?

Given a simple 2dof system, why would you expect to not be able to excite a resonant response, given control over one dof?

There's no problem setting up a resonant response in the vertical direction, but in the absence of any horizontal forces, the movement will be on a vertical line through the centre of mass.

Sorry to be so repetitive, but as far as I can see no-one has addressed this point.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[SomptingGuy]

Hmm, I wonder if the deflection of the chain comes into play? As a kid I always remember that standing on the seat made things happen more quickly.

- Steve

 

[rb1957]

zekeman,

newton and several posts here, has already covered your question. a body at rest remains at rest untill acted upon by an external force. in the case under question, the kid on the swing moves his legs, and energy (work) input into the system and the rest is Newtonian motion.

greg,
your model starts very slowly, and you suppose kids would get bored, and so the real world is different. last time i was on a swing, i backed up so i wasn't under the suspension point of the swing, (still at rest zeke, supporting my weight on my legs) and let go ... and went from a position of rest to one of motion ...

 

[HamishMcTavish]

I haven't been on a swing for a long time but from memory (and me sitting in the office acting this out much to the amusement of the dog...) "working up" is achieved by the person standing and using reactions between the seat, the persons body and the chains holding the seat off the ground. Push your legs out (body bends) bracing with the arms and then quickly straighten body, do this a few times and then sit and use the legs as indicated earlier in the thread!

Cheers HM

No more things should be presumed to exist than are absolutely necessary - William of Occam

 

[zekeman]

OK,
Let's assume that you model the swing as a pendulum with a large bob, enough to enclose the kid. Now tell me how it is possible to move the pendulum from its vertical rest position.
My answer is that , in the absence of friction, you can't, since you are starting out with zero angular momentum with respect to the pivot and there are no external forces that can produce a torque .
So preserving angular momentum and it starts at zero it remains at zero and the CM won't move.

 

[SomptingGuy]

The "F" word.

- Steve

 

[TenPenny]

If your model doesn't allow the swing to move, then your model is wrong.

All the kid has to do is start moving his/her body, and the swing will start moving.

So, the problem is that the model doesn't accurately reflect reality.

 

[rb1957]

"in the absense of friction" ... last time i checked we had friction, and if we didn't we'd be in a very bad way.

let me say this simlpy, the kid is adding work to the system. if the kid was a quadruplegic, he'd have a very hard time of it (not only starting a swing but most other things as well). if the kid (with legs) sat there and did nothing; well, nothing would happen. by swinging his legs and pulling back on the swing ropes, he gets the swing going.

btw, is this a wind up ? (no pun intended)

 

[Tmoose]

http://news.nationalgeographic.com/news/2006/09/060928-cats-land-video.html

 

[btrueblood]

"How can you accellerate the centre of mass of the system (everything below the pivot) if there is nothing to provide a horizontal reaction?"

The kid, by moving his legs with respect to the rest of his body, changes the position of his center of mass in space. The swing moves, because the c.o.m. has shifted.

"Let's assume that you model the swing as a pendulum with a large bob, enough to enclose the kid. Now tell me how it is possible to move the pendulum from its vertical rest position."

If the kid can move within your plumb bob, then he can shift the position of the center of mass of the system, either by moving parts of his body (legs, arms), or by moving himself relative to the rest of the swing/bob.

If those concepts give you trouble, then tell me how a rider on a bicycle can generate forward motion...after all, angular momentum must be conserved, and all he's doing is rotating a crank.

 

[ione]

We have to think to the whole system (swing + kid). It is not a rigid body system. As stated by btrueblood the kid, who is a part of the system (a living part of the system I’d dare to add) moves his legs forward and back and changes the overall system configuration, that is he/she changes the mutual distance of points (masses) which constitute the system. Thus the position of the centre of mass of the whole system is changed. And then something called conservation of angular momentum starts to do its job.

 

[btrueblood]

"My answer is that , in the absence of friction, you can't, since you are starting out with zero angular momentum with respect to the pivot and there are no external forces that can produce a torque .
So preserving angular momentum and it starts at zero it remains at zero and the CM won't move. "

and another post stating "there is no horizontal force that can act" on the pendulum.

Again, as previously stated, angular momentum of a system is conserved IF no external forces (torques) act on the system.

Yes, there are horizontal components of force that can, and do act, on a pendulum. The external force acting is that of gravity, and the horizontal reaction forces transmitted through the pivot point of the pendulum (the reaction force is equal and opposite to the force that the kid exerts to move his legs to-and-fro). The forces are developed as soon as the c.o.m. is shifted from the nominal vertically-aligned or zero position. Once some angle theta exists between local gravity vector and the line between hinge and center of mass of the pendulum, the horizontal restoring force acting on the "bob" of the pendulum is exactly
mg*sin(theta).

 

[berkshire]

true blood,
Now you are thinking my way,

""The forces are developed as soon as the c.o.m. is shifted from the nominal vertically-aligned or zero position. Once some angle theta exists between local gravity vector and the line between hinge and center of mass of the pendulum, the horizontal restoring force acting on the "bob" of the pendulum is exactly mg*sin(theta). ""

B.E.

 

[btrueblood]

Never denied it, Berks.

"So preserving angular momentum and it starts at zero it remains at zero and the CM won't move. "

...E pur si muove!

 

[KENAT]

Vaguely analagous might be to consider a typical medieval trebuchet.

If a rigid mass is used for the ballast then when fired, as well as the vertical load taken by the main structure, there is also a horizontal load due to the CoG of the mass moving horizontally as it inscribes an arc.

It is for this reason that typically they either have wheels to allow some horizontal motion, or (and probably better for accuracy) they have the ballast hanging from a pivot.

In the case where the ballast is rigid, and the trebuchet is on wheels, the fundamental system is not that different from a kid on a swing lifting and lowering their legs. The CoG/CoM of the kids legs inscribe an arc a bit like the mass on the arm of the trebuchet. This gives you a horizontal force to get you swinging.

The big difference is in then repeating this swinging motion at somewhere around the natural frequency of the swing with the impulse in the right direction at the right time.

Posting guidelines faq731-376

http://eng-tips.com/market.cfm?

(probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484​

 

[ChrisDuncan]

I'm with EngTex on this one, it's friction in the system that allows a start from a dead stop, and it's very hard to start a swing that way. You are trying to move the CG away from dead vertical to get it up the arc so gravity will pull it back down. The only thing you have to push against is the friction at the pivot of the rope/chain. In the case of the rope it's the friction within the fibers themselves. Once it's moving I think more of the inputed force comes from bringing the mass closer to the arc center on each swing, than from shifting the CG. Like an ice skater that increases spin speed by centralizing mass. This has to happen in a timed fashion, you move the mass away from center as the swing peaks and move it back towards center, by bending the rope, after you've picked up some speed on the down slope.