Discussion in 'Off Topic [BG]' started by Bassline_Delux, Jan 18, 2006.

1. ### Bassline_Delux

Dec 24, 2003
London, England
I don't suppose anyone knows the equations of motion for a slinky? Or each of the coils. Please. Help.

Apr 13, 2001
berkeley, ca
i wouldn't even know where to start, really.

they aren't quite springs...

my guess is that any motion of a slinky is extremely hard to describe.

sorry.

...geoff?

3. ### nateoSchubie Fan #1

Mar 2, 2003
Ottawa, Ontario
They're exactly springs, they've just got a resting length equal to their minimum (i.e. fully compressed) length. You stretch them out, they pull back, just like a good spring should.

In terms of equations, I don't really know what you're looking for. Oscillation equations would be easy to find (i.e. you stretch it out, move one end, and see how the wave propagates down the slinky), but the bending / walking down stairs equations would be a bit trickier.

What exactly are you trying to figure out / prove / disprove / teach here?

-Nate

Apr 13, 2001
berkeley, ca
ah, you're right. it is a spring.

i'm just trying to imagine how to treat a slinky going down a set of stairs.

5. ### MikeyFingers

Aug 1, 2005
Long Island, NY
I think it's just the rule of "every action has an equal and opposite reaction" (Newton).
The motion of it falling from one step to another (step 1)creates enough stored energy (step 2) to spring the slinky back up in the opposite direction (step 3). When the slinky bounces in the opposite direction from which it came, gravity pulls it down to the next step and so on.

(Now you know I'm serious with that "what should I do today" thread. I'm so bored I'm drawing diagrams overhere...and drawing them very poorly too)

6. ### nateoSchubie Fan #1

Mar 2, 2003
Ottawa, Ontario
I think the energy stored by compressing the spring will be minimal, since the resting length doesn't allow for much compression. The way I see's it, walking down the stairs would go something like this:

1) The top end of the slinky is pushed over the edge.
2) It falls, pulling more slinky down to the next step.
3) The tail end of the slinky is pulled over the edge, but momentum carries it beyond the main body of the slinky and over the next edge, repeating the cycle.

To work out equations of motion for that cycle, you'll need to know the spring constant (to determine how much force will be exerted by stretching the spring a certian length), the mass of the slinky per unit length, and the geometry of the steps. I would think that with a bit of calculus that should give you a good initial approximation, though to get an even more accurate estimate you could figure in what the bending of the slinky does to the motion. If you were some sort of physics freak, the next step would be energy transfer as one coil hits another, the effect of air resistance, the loss of energy due to contact surfaces (carpet vs. lino), etc. The only problem with that is that if you put that amount of time into it I'm going to make fun of you for weeks.

Of course, it's been a while since I was registered in a mechanics course (and even longer since I attended one), so I could be way off base.

-Nate

7. ### Geoff St. GermaineCommercial User

Nateo's right. Start at the equations of a spring. Finding an actual value for k may be tricky for a slinky. I'd just model it as a damped oscillator.

What exactly are you trying to do? Do you want to model it walking down the stairs? Then you'll need to add a term for gravity adding potential energy to the system. Overall it is actually going to be a fairly complicated problem.

8. ### Geoff St. GermaineCommercial User

I agree, it's mostly a case of the momentum of the slinky than of the slinky acting like a spring a bouncing down the stairs.

I've never had a slinky, but what happens if you just hold the slinky extended above the floor and drop it straight down? My understanding is that it just hits the floor and doesn't really bounce very much. I could be wrong though.

9. ### AaronS

It tips over and spills out over the floor. The Slinky as a toy was an idea that came to a fellow (a Naval officer during WWII IIRC) watching a spring move on a desk or something like that. I don't remember all of the story, but I'll bet you could google it. Geoff, I was wondering when somebody would mention that gravity is an important component!

10. ### zac2944

Dec 28, 2004
Rochester, NY
I wouldn't try to describe the motion of a Slinky with equations of motion. If the Slinky was flying through the air at some known velocity or if it was in free fall or something the equations of motion, or "kinematics" as they are commonly called, would be a good place to start. The Since the Slinky is usually traveling down stairs, kinematics won't work.

Your best bet would be to use the law of Conservation of Energy to describe the motion of the Slinky. COE is my favorite physical law, it really kicks ass and can really make complex problems very easy to solve. The key is that you have to look at the Slinky as a whole. Do not try to break it up into coils or anything like that unless you have a masters degree in engineering or physics.

When you start the Slinky at the top of some stairs you have to stretch the Slinky, or "spring" to get it started. This is the Slinky's "initial" position. This energy required to stretch the Slinky, plus the height on the Slinky relative to the bottom of the stairs is your total initial potential energy. You have no initial kinetic energy because the Slinky has no velocity. This total initial potential energy will be equal to the total final kinetic energy that the slinky has when it reaches the bottom of the stairs.

I haven't done this stuff in years, but your equation would look something like this:

PEi + KEi = PEf + KEf

where: PE = potential energy, KE = kenotic energy, i = initial, and f = final.

You should be able to get it from here.

Good luck.

11. ### Geoff St. GermaineCommercial User

The equations of motion will work fine for this problem (and equations of motion are not specific to kinematics, they work for dynamics too). They may be complicated, but it depends what he's trying to accomplish, which he hasn't spelled out yet. It could be walking down stairs or across a floor. There could be longitudinal or tranverse waves. The slinky is really a toy with diverse applications.

If I were to actually work a problem like this, I'd probably want to use Lagrangian mechanics anyway, but I don't know how many people here even know what that is, much less how to work problems with it. Seems to me that I worked something similar in classical mechanics, some sort of mass-spring-pendulum system. I recall it taking many pages and hating it.

12. ### Tsal

Jan 28, 2000
Finland
Hmm. I don't know, but I would suggest the motion comes from the topmost part of coil having enough energy from toppling over the side and pulling the whole coil inch by inch with it. Obviously, if going down the stairs, the coil needs to have enough movement energy to bounce the rear end over the toppling point of 90 degrees (?) again.

I really haven't played with a slinky, though, so I can't say anything specific from it's behaviour

Apr 13, 2001
berkeley, ca

yeah, exactly.

now off to my mechanics class!

14. ### zac2944

Dec 28, 2004
Rochester, NY
Basline Delux, you really need to better explain what it is you want to know.

Geoff St. Germaine seems to know everything, but since none of us are as smart as he is it might not be much help to you.

Good Luck.

15. ### Geoff St. GermaineCommercial User

I am a physicist, so I tend to know a little about physics.

16. ### zac2944

Dec 28, 2004
Rochester, NY
Sweet. I'm a mechanical engineer, and everyone knows engineers are smarter than physicists.

That was a joke. But seriously, don't assume that no one here is as smart as you are. According to your profile you're only 24. It's not like you're Einstein.

According to Bassline Delux's profile he's 20. I would bet he's in his second semester college physics class and this question came up. Conservation of Energy is usually tought in this calss and teachers typically introduce it by showing how it can be used to boil down a seemingly complex problem. I doubt he would be asked to use Lagrangian methods to solve the problem. But it did make it sound like you "know a little about physics".

17. ### nateoSchubie Fan #1

Mar 2, 2003
Ottawa, Ontario
Awesome, then I must be smarter than the lot of you. Or, at least, smarter than myself.

Naw, who am I kidding, I was the worst student ever. Remember me as a student, Geoff? On the other hand I kicked ass at being a slacker. You gotta do what you're good at, I always say my mother used to say.

-Nate

18. ### Alex

Watch out, Renoir and Monet - here comes Mikey Fingers!

I especially love the spring illustration, so accurate and precise....

19. ### Geoff St. GermaineCommercial User

I never assumed that. When did I? Because I said I don't know how many people know how to use Lagrangian mechanics? Well, I don't know, and it is safe to assume that most don't. Nowhere did I say that no one else can. I know that there are several people who can (Nateo and Brad Barker for sure). I'm sorry if you read it the wrong way, but there was no insinuation that I'm smarter than everyone else (how does knowing a problem solving technique show how smart you are anyway?), and some people may have heard of it, but wouldn't have seen how to use it (like myself when I was in my second year of my undergraduate degree before being taught the method).

When did I say I was Einstein. You shouldn't make so many assumptions, they're offensive. Especially with your "talking down" attitude.

20. ### SnoManWords Words Words

Jan 27, 2001
Charleston, WV
Apparently we may need a physics forum in the lobby.

Then it can get closed down for the same reasons as TPA.

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