We took SteelyKid to the playground at one of the local elementary schools on Sunday morning. this one includes an odd sort of slide, made of dozens of rollers that are 1-2 inches in diameter (they're all the same size-- the range is just because I didn't measure them carefully). They're on really good bearings, and while it's kind of noisy, it's a reasonably smooth ride.
There is, however, one slightly mysterious aspect to this slide, clearly visible in this video that Kate was good enough to shoot for me:
SteelyKid takes something like 6 seconds to go down the slide, while it only takes me about 2 seconds to reach the bottom. This is kind of surprising, as it's the reverse of most of the other slides we go on-- usually, she handily beats me to the bottom on any set of parallel slides.
It's also not what you would expect for an idealized slide from introductory Newtonian physics. The acceleration of an object sliding down a ramp, even with friction, should not depend on the mass of the object. And yet, I very clearly go faster than SteelyKid does, and while I don't have the video to test it qualitatively, I'm pretty sure Kate's rate of sliding falls between SteelyKid and me.
So, the question for you is: Why does that happen?
After a bunch of playing around with Tracker Video (I probably owe Rhett a dollar for blog infringement), I have a possible theory, but I'm really not 100% sure what's going on here. So I'll throw this out to my readership: Why do I go down the roller slide so much faster than SteelyKid does, when that's not what happens on a regular slide? Leave your theories in the comments, and I'll post my analysis and my guess at the answer later in the week.
(Also, the "Go, Daddy, go!" from SteelyKid after she exits the frame is totally worth uploading this to YouTube in its own right...)
- Log in to post comments
I bet if you both sat on a solid board, you would descend at the same rate. Maybe it has to do with your posteriors having to deform as it travels over each roller. Might be something like energy lost due to butt deformation vs. potential energy.
Hmm... something about the moment of inertia of the rollers, and you providing more energy to overcome it?
Watch her little shoes. She's hitting every roller with them, while you aren't.
The way this slide presumably works is that you provide a net torque on the roller, which pushes you on to the next roller. You are quite a bit heavier than SteelyKid, so you put more torque on the rollers, which therefore rotate under you faster and push you down the slide faster. Whereas on a standard slide, your larger surface area means more friction, so you don't slide as fast as SteelyKid does (the mass tends to cancel out in problems of this kind, so something of SteelyKid's dimensions and your mass would slide as fast as she does on a standard slide).
To me, it seems like your feet are starting the rollers ahead of time, so by the time your butt hits them, they are already moving and they just start to move faster, while Steelykids feet are not as far ahead of her and don't have as much effect. Kind of a conveyor belt effect(where your body is the belt)
Argh, Sideshow Bill got there before me.
Agree with Bill entirely, she's slowing herself down, whereas you're aiming for speed.
I was thinking along similar lines to what Derek R said, but then it occurred to me that your butt deformation coefficient would be higher than SteelyKid's, so you should go slower, not faster. But I do agree with Derek that if you both sat on a solid board, your rate of descent would be the same. So the butt deformation coefficient has to play into the equation somehow...but how.......? Hmmm. Needs further study.
Since neither one of you is moving as fast as you would on an ideal slide with zero friction, the difference comes from each body's ability to overcome resistance. I think in the case of a roller bed, the greater friction/traction of the more massive and larger contact surface body are a more efficient lever, and the greater mass overcomes the inertia in the rollers plus the friction in its pins. The smaller, lighter body is not transferring enough energy to turn each roller.
Also, too, the shoes as noted above.
I think SK hits terminal velocity almost straight away, and you're still accelerating to the end. At terminal velocity, the rollers are soaking up all the energy: g x mass_of_slider x delta-h (per roller). The "mass of slider" term says you have a higher terminal velocity than SK.
On an ordinary slide, total friction is (supposedly) prop. to mass, so you and SK should have the same acc & TV.
Supposedly.
In reality, friction usually increases more than linearly with pressure, and you do have higher pressure than SK does (3/2 power[1] of height).
[1] Assuming you and SK are both sphe... the same shape. ;-)
A slide is a device for converting gravitational potential energy into kinetic energy. On a standard frictionless slide, the mass of the slidee doesn't matter, as the mass cancels out. With the sliders however, some of the GPE goes into rotational energy, and this depends on the speed at which the slidee goes over the roller, but not their mass. You have a lot more GPE than SteelyKid, so the loss of energy to the sliders slows you down by a smaller amount.
I suspect it's the result of rolling friction and inertia. You have to overcome friction, of course, and rolling inertia. Your increased mass means you can overcome inertia time and again, whereas your daughter can't.
Also, I agree that "Go, Daddy, go!" is ridonkulously adorable.
Extra points for discussing Chad's butt.
Before I watched the video, my vote was with Anna B at #2 and SimonW at #10 (assuming the description of "really good bearings" is correct).
If there's no slipping of the slider on the rollers, and the rollers have a nonzero moment of inertia: then in the limit that the slider mass goes to zero, the velocity will go to zero.
But after watching the video and reading Sideshow Bill's comment at #3, it's hard to tell which is the dominating effect. To distinguish between them, you could do some experiments with the rollers to determine their moment of inertia, and then do some math to figure out how big an effect it would be for both of you. Or you could do some experiments trying to persuade SteelyKid to position her feet differently (way to spoil a fun outing, dad!). Or just bring some dummy weights to the slide, and watch their speed vs. mass.
I'm with the camp that says you overcome the moment of inertia of the wheels with more torque and hence more acceleration. I wish they had this kind of slide when my kids were little.
My experience with this slide goes back to my summer job as a Canada Dry soda delivery guy and we would use this type of slide to avoid going down stairs to the basement. Some even had a curve at the bottom of the stairs and the cases would pile around the corner. if you did not pay attention you would break an entire case of glass bottles or explode some cans. Messy either way.
You don't appear to speed up as you go down, so you might have pushed off more than SK did so that you started with a higher initial velocity. (Is that what you were looking at with Tracker?)
It's definitely the rollers that change the speed. When my nephew was little there was one of those slides where we took him to play. He didn't have enough weight to get the rollers moving like somebody bigger would. Normally mass wouldn't make a difference, but you get those rollers going, and by the time YOU hit the bottom, they're flying.
In the video there is clearly a lot of vibration of the child's legs, presumably caused by adhesion to the surface of the slide. The threshold of force needed to overcome this adhesive resistance would be crossed more easily by a greater mass, even if the adhesive resistance is equal between the child and adult. Other factors might make the resistance for the child greater than that of the adult, for example smooth hairless skin vs. hairy skin. It also appears that you leaned back a bit, distributing your weight more upon the seat of your pants than on the legs. If the child lifted his legs even a millimeter off the slide surface, or perhaps wore long pants, he would probably slide at the same speed as you.
I would guess that the difference is that on the rollerslide, you are imparting momentum to each roller as you hit it, whereas on the regular slide you are losing your energy to friction rather than transfer.
On a standard slide, your larger surface area slows you, and your increased mass means a larger friction force. On the rollerslide, your surface area becomes irrelevant because the friction is in the bearings of the rollers, rather than between you and the surface. Further, your greater mass means more momentum, allowing you to spin each roller at a lower cost to your own speed (than a smaller, lighter child.)
Of course, that's all off the top of my head, and I'm not engineer or physicist.
I'm not a physicist, but I assume the butt deformation coefficient is a standard physical constant.
BTW, on normal slides, does SteelyKid have less friction because her butt deformation coefficient is the wrong value to let her touch both sides?