Why does tucking your legs make you swing higher?

[T@P]

as a child i remember swinging in the playground, and i knew somehow that keeping your legs straight on the way up, and tucked in on the way down would make you go higher. I was wondering exactly why this is true, is it something to do with the moment of inertia? just a thought

 

[Tide]

This is an example of a parametric oscillator. The swing has a natural frequency (it's just a pendulum) and by raising and lowering your legs in synchrony with the natural oscillation you cause the amplitude of oscillation to grow. The pendulum's length is being varied periodically and resonantly.

 

[Integral]

Haven't you neglected a key companion to the leg motion? As you straighten your legs you lean back, as you curl your legs you lean forward. The combination of these motions results in a vertical shift of your center of mass. It is this change in potential energy which must be synchronized with the natural frequency of the swing.

There is another little factor, notice what happens to the swing when you are getting started from a dead stop (no push off from the ground) As you lean back you create a bend in the support lines at your hands. This action tends to lift the seat a bit, giving you a small potential energy change which converts to a small bit of rotational kinetic energy. Thus starting the motion.

 

[Cyrus]

Thats such an interesting problem. It seems that you have started motion with no external forces, since you are part of the system itself!

 

[Ivan Seeking]

You are pulling against the swing supports through the chains or rope and doing work by lifting yourself; really pivoting about the point where you hold the chains.

 

[Integral]

Cyrus,
The shift in your CM is a change in PE. Your body does work when you change your position. It is this work that changes the PE that is converted to KE.

I think a key factor in starting from a stop, is the ability to create a shorter pendulum between your hands and the bottom of the swing. When observing this shorter pendulum the change in height of your body is clear, this change in height is constrained to a rotation around your hands, the resulting horizontal motion is then fed to the larger pendulum and the oscillations begin.

It would be interesting to see if you can self start a swing with rigid supports.

 

[Tide]

Integral,

I suspect that would not be possible if you started with absolutely no displacement or speed for your initial condition. However, in the physical world there will always be some fluctuation, no matter how small, and the parametric oscillator will eventually amplify those fluctuations.

 

[Cyrus]

you say you change your PE relative to your center of mass. Do you mean that you simply raise your body up, or does there have to be a side component as well? It seems that changing your PE is not enough to start motion, because you could sit there lifting your body up. I would think you have to move both forward/orbackwards and up at the same time.

 

[Tide]

Cyrus,

See my previous post! :-)

 

[Cyrus]

your post is eye opening tide! But I do remember being able to start a swing moving from a dead stop when I was a little kid. It involved leaning way back until your whole body was nearly horizontal and then going back to an upright position. I see what you mean by not being perfect though. Gotcha

 

[Cyrus]

Hmm i have anothere question tide. Are you sure its not possible to start from a dead stop? Suppose you lift yourself up with your arms on the ropes. (your arms are bent in the process.) Now while in the air and holding on, you unbend your arms. Now you are pushing out, but the swing reacts and moves away. So you are now in mid air, holding yourself up, leaning back, while the swing is leaning forwards. Your not swinging, but your just sitting in mid air like that. Then you bring your arms back in and bend them. Wont this induce swinging from a dead stop?

 

[Tide]

Cyrus,

My comments on whether you could build amplitude from a dead stop were in reference to the RIGID structure Integral mentioned. I don't think there is any question about being able to pump up in the case of flexible ropes or chains.

 

[Cyrus]

Hey Tide,

But even for a RIGID structure, could the same argument not apply? We are now on a rigid swing. You grab each bar of the rigid swing and lift yourself up so you are suspended. Push with your arms until they are locked. Wont this force the rigid swing to pivot forward as you push on it. Either that or it will remain in place and you will move back depending on how heavy it is. I guess if it were heavier than you are, then you could never get it to swing no matter how hard you tried, because you would just move back and it would sit there. Anyways, let's assume its much lighter than you are and it does move forward. Then can't you simply relax your arms and it will swing back to its origonal position, but now with speed since you raised its potential energy. You can then let go and fall onto the chair when its beneath you and thus induce swinging even on a rigid body? Once you fall onto the chair it should continue moving but with less speed, becaus that is simply an inelastic collision, and if you time it right so that the chair is passing exactly below you when its at an angle of 90 with the horizon, then momentum is conserved in only the x direction at that instant of impact. And that would just be: m1v1 = (m1+m2)v2, with v2 now being smaller than v1 because the mass increased?

 

[Cyrus]

Another point i forgot to add. Let's say this swing is RIGID. We start off in equilibrium. Then the child holds him/herself up in the air by grabing onto the columns, and then pushes out with his/her arms. Now there is a force produced by the child that will produce a torque. If the colums and seat are not to heavy, then the swing should start to pivot. I would guess that it did not pivot all the way, because the girl my move backwards as well, but it might be some combination of the two occurances. Now its bed time, I look forward to your post in the morning on how I am all wrong :-) Good night.

 

[Tide]

Cyrus,

That sounds a little like the "cat always lands on its feet" argument which seems to defy conservation of angular momentum - but it works (provided the cat has enough initial height!) and angular momentum conservation is safe!

Your proposal may work. Maybe we can get some grad students to do an experiment ...! ;-)

 

[KingNothing]

Grad students my butt. Give me a week to make a rigid swing. On the other hand, I don't know anything about parametric oscillators or pendulums or frequencies, or waves, although I would like to learn about it, because it sounds very interesting.

On another note, what would be the best way to go through with an experiment like this? I was thinking about taking some 8 foot long metal rods and sticing them through the chains on a playground set and using some wire to make sure the chains stay rigid to it. Then just take a strong piece of 2x4 and duck tape it onto the seat real good and try it. Would that accurately reconstruct the scenario?

 

[krab]

You don't need to actually build one, since the physics is so simple. You can build a virtual swing using sodaplay (www.sodaplay.com[/URL]). I simulated a child on swing as an equilateral triangle, with one of the sides as a muscle, and the top vertex fixed in space. The muscle oscillates sinusoidally, and so if this frequency matches the natural frequency of the triangle as a whole (acting like a pendulum), the whole thing begins to swing back and forth. To look at it, go to

http://sodaplay.com/constructor/?getmodel=krab+swing

The controls at the side allow you to change gravity, frequency, friction, and the rigidity of the other two bars of the triangle. The upshot is that if starting from a dead stop, it does begin to swing. The best technique is to first set the frequency to zero (the control is the thingy on the left edge at the top), and then slowly pull it down until it is in resonance, which will be at about a quarter of the way down. Have fun. (BTW, you need Java.)

 

[T@P]

wow krab that model is very interesting, thanks a lot! thanks to everyone else that posted too, your thoughts were very usefull :)

 

[T@P]

actually i was playing with krabs model and i noticed that when i turned off gravity, it always made i way up to a certain height and stayed there, regardless of where i started "stopped" gravity. can anyone explain that?

 

[Cyrus]

krab can you explain how your model works. I am a little confused in understanding how it works. You seem to have made a triangle. It looks as if the right side of the triangle is the rigid pole of the swing. The left side is a little confusing though. It seems to be oscillating, but it is also attached to the pivot point. Shouldent it be attached only at the very button where the person would sit? Thanks,

 

[KingNothing]

I had great aspirations of hurting my bottom on a rigid swing, and they have just been ruined by a model I don't really understand.

 

[Tide]

I had great aspirations of hurting my bottom on a rigid swing, and they have just been ruined by a model I don't really understand.

Yes, but what is simulation compared with a real life experiment? Go for it! :-)

 

[krab]

krab can you explain how your model works. I am a little confused in understanding how it works. You seem to have made a triangle. It looks as if the right side of the triangle is the rigid pole of the swing. The left side is a little confusing though. It seems to be oscillating, but it is also attached to the pivot point. Shouldent it be attached only at the very button where the person would sit? Thanks,

It's a minimal swing/swinger. The one side of the triangle oscillates in length, thus oscillating the position of the centre of gravity. That's the essential ingredient. Notice if both sides oscillate in phase (there are two little bars in the area just above the letters g,f,k. These correspond to the other two sides of the triangle. Move one up into the area where the sine wave is oscillating. If they are at the same location, they are in phase.), then no swing action starts because of the symmetry. This shows that the key ingredient is the horizontal component of the c.of.g motion.

I guess if you want the closest real-life analogue, it would be the case where the person stands on the seat, with ass out, while holding on with hands near the pivot point, and flexes arms or legs.

 

[Rogerio]

...
It would be interesting to see if you can self start a swing with rigid supports.

You can start the swing by flexing your legs, even with rigid supports.

 

[Cyrus]

Thank you for clearing it up krab. I never dealt with a problem concerning a changing center of mass before. How would I go about determing the force that is imparted as the center of mass of an object changes? Right now I am just guessing, but I would think that if the center of mass moves, then the force would be F=ma, directed in the direction of motion? So if your on the swing, ass out, and you move your bum in. Then your center of mass moves inward. So the force also moves inward. But your center of mass is somewhere near the middle of your torso. So how would I represent this force on the swing? Where would the force be acting along the length of the swing.