Posted by Larry Hoover on April 24, 2005, at 22:33:32
In reply to Re: Well, come join me on the swings then... » 10derHeart, posted by alexandra_k on April 24, 2005, at 18:50:10
> And I'm sure Damos will give you a push.
>
> Incase anybody knows...
>
> Is it possible to swing right round over the top?
> Or will you get up there in the air and then just splat down again?
> Or is either option somehow prevented?
> I worry about this a lot...You can swing too high, and because the chains are flexible, there is danger in swinging above the horizontal.
A stationary swing is set in motion by moving laterally. The tension of the chain pulls the lateral motion into an arc, and as a result, you get lifted above the starting position. This lift is potential energy, which is really the option for gravity to pull you down again. As you fall down, you pump your legs, and you increase the height of the forward arc. This lifts you higher, and potential energy swings you back again. Kick, swing, kick, swing, and the higher you go.
If you picture being at the maximum height on the backswing, your kinetic energy of motion is completely turned into potential energy (you stop going back, and for an instant, you haven't started going forward yet). At that instant, the force of the chain holding you in the arc is at its minimum. As you start to move forward, your potential energy turns to kinetic energy again, and you pick up speed until you're at the very bottom of the arc. At that point, the force of the chain pulling you in towards the centre (centripetal acceleration is the result of that force) is at a maximum. As you rise forward, kinetic energy again turns to potential energy, and the tension on the chain goes to a minimum again.
The mathematical relationship of the tension on the chain (the inward force that keeps you from flying off in a straight line) varies as a trigonometric function of the angle. At exactly 90 degrees forward motion (true horizontal), your forward motion goes precisely to zero.....and if your kinetic energy goes to zero at exactly that point, you are completely weightless.....for an instant.
The key point to consider is that the tension on the chain also goes to zero at this horizontal extension, if your upwards motion stops too. If you're not moving, it's not pulling you inwards, for that instant, either.
If you go above that critical 90 degree juncture, the chain tension never goes to zero. Instead, it starts pulling you backwards again. If it pulls you backwards while you're still going up, the chain will go slack when gravity starts pulling you back down. You won't be travelling in an arc any more. (Mathematically, you'll follow a secant to the arc.)
When I was a kid, we called that "getting the bumps". The chain sags, and you literally fall free for an instant, until the chain snaps to full tension.
If you are not careful, rising about 3 degrees above the horizontal is sufficient to risk causing you to fall off the swing seat, and as the chains snap taught again, your grip will be broken, and you will tumble off, backwards.
Lar
poster:Larry Hoover
thread:485504
URL: http://www.dr-bob.org/babble/social/20050418/msgs/489058.html