Hill into sidewalk, snow, sled. Kid zablooms down the hill, skids over the sidewalk (no snow), into the street (no snow) hits far curb. Is ecstatic, leaps in air claiming to have taken that sled where no kid has taken it before, in the world’s unbeatable longest ride.
His pals on the top of the hill immediately start pissing on his parade: “no fair, you weigh mor than any of us, that’s why.”
Me, passing by: “Gravity works the same on feathers and bowling balls, excluding wind and other stuff. Look up the vid on the moon. Anyway, trust me, Galileo. Tell them to go suck it.”
Best part: kid yells up at other kids to go suck it, Galileo said so.
Did I lie?
I checked if each kid started from a sitting start–they did. So did the factor of inertia screw me up, and I lied to the hope of America’s future?
I think you’re pretty much right. You said ‘gravity works…’ and there’s no quibbling about that. To pedants who’d say ‘what about air resistance, friction…’ you’d say ‘well they aren’t gravity are they?’
“gravity” =/= “how things fall”. It’s the most important part for a fat kid on a sled. There are other parts. But they aren’t gravity. Even when we look at a feather, and gravity is no longer the most important force in considering how it falls, it’s STILL true that gravity induces exactly the same acceleration on the feather as the bowling ball.
Plus, even if you’d been more careless and said “the rate of fall of a body doesn’t depend on its mass”, you’d still be right because of the qualification you added, “excluding wind and other stuff”. Of course then, your correctness would really be a tautology.
Even if we then say, ‘okay let’s actually talk about the motion and take care to include all the non-gravitational forces (basically friction with the ice and drag with the air) to calculate the kid’s average velocity and/or duration and length of ride’, then:
To a first approximation, who gives a fuck? He is a fat kid, NOT a feather. Those corrections are small beer.
To a second approximation, his extra mass will INCREASE the force of friction, so if anything he is at a DISADVANTAGE compared to lighter kids.
To a third approximation, I’m not sure how his mass affects drag, but I suspect a roughly spherical shape is pretty decent aerodynamics at those sorts of speeds.
But it was the OP who brought up gravity, not the fat kid or his friends. The fat kids friends said he went further because he weighed more. I think that is very likely a true statement.
But the OP asked if they, the OP, lied. So we should be talking about what the OP said, not what the kids said. As for the truth of what the kids said, I addressed that in what you probably missed in the cross-post.
Heh, true. In everyday language and in fact in most sciences, one can get away with carelessly conflating ‘mass’ and ‘weight’. This is mechanics, which is precisely the field in which they must be distinguished (at least if you want to apply Newton’s laws sensibly).
At least for snow, your assumption about friction is incorrect. Assuming all the kids were using the same size sleds, the fatter kid will exert a larger pressure on the snow, which tends to decrease the coefficient of friction.
And I suspect that the friction force between the snow and the sled is the main factor in determining how far he slides.
Interesting link. I don’t think it changes my basic conclusion for a few reasons.
I accept that I didn’t consider that the extra weight would reduce mu. To the extent it does, then friction is reduced. BUT, F = mu N. The normal force is still increased. So the decreased mu and increased N work against each other. I can’t say offhand which would prevail.
But I still think that, regardless of which would prevail, the friction WASN’T the main factor in determining how far he slid. Friction between a sled and snow is tiny. That’s kind of the point of sleds and snow. We know he must have built up some speed because the OP said he went over two high friction surfaces and still hit the kerb.
So actually the main factor in determining the distance was… the existence of the kerb! Now had it not been there, with the sidewalk and street, the high friction THERE would have slowed anyone down sharpish, but probably the fat kid more than most.
Uh, if you assume mu is constant, yes, the friction will be higher for the fat kid, but so will his momentum, and they would exactly cancel each other out. If the mu decreases for the fat kid, then he will slide farther because his higher momentum will more than offset the higher friction.
This is easy to test. I’ve done it many times. Slide down a hill. See how far you go. Add some weight to the same sled. It’s most fun when that weight is another person. Now slide down again. See how far you go. You’ll go farther (usually. Can depend on the snow conditions. With very light snow it can sometimes be better to have less pressure so you don’t sink in as much. Usually not the case though, in my experience, especially after you and some others have gone up and down the hill a few times)
From your context, it seems clear that the fat kid was able to make it further than all the not-fat kids. Now we don’t know all of the factors: maybe he had a better sled or a faster running start. But without being there, I am guessing that his weight was a significant factor.
The kid must have actually gotten an obviously longer ride than the others, because his friends didn’t try to dispute it and blamed it on him being fat.
If everything else were truly equal, and the only difference was the mass of the two sledders, then it seems like the only reason his ride was longest is due to his weight, regardless of the underlying physics of why that came to be.
So what message were you trying to send to him? That it’s okay to be fat because gravity? Or that he won by some magical force since the only thing different was his weight? Something else?
You were wrong, the kids on top of the hill were right.
A heavy thing at the top of the hill has more potential energy than a light thing. Yes, a bigger (and heavier) thing will have to overcome more wind and sliding resistance than a smaller and lighter thing to slide to the bottom of the hill, but the increase in those resistances will cause only a relatively marginal drain on the energy of the former. Meanwhile, the heavier object has substantially more potential energy that is being converted into kinetic energy as it drops. The end result is the heavier object will fall faster because it has the greater imbalance between the potential energy it is releasing as it drops and the energy being lost to resistance, and then it will continue further after reaching the bottom of the hill because it will be going faster and take longer to spend its kinetic energy on friction before it stops.
You can also look at it in terms of force: the rate of acceleration of the respective kids downhill is proportional to their respective masses, and the forces on them. The gravitational force on each kid is precisely in proportion to their masses, which means that leaving aside friction, their accelerations would be the same. But you can’t leave aside friction and while the increase in resistive force on the heavier kid is slightly higher, he has heaps of gravity to overcome that. Meanwhile the lighter kid gains through having slightly less resistive force acting upon him, but has substantially less gravitational force to overcome that.
End result is the heavier kid will accelerate faster and then slow down slower when he gets to the bottom.
This topic causes endless debate. As I’ve commented before, it’s one of those topics which generally smart and somewhat science educated people sometimes get spectacularly wrong because they know just enough to be dangerous. They’ve heard of the cute feather/bowling ball thing and are determined to show how smart they are by applying it in circumstances where it just can’t be applied.
There is a (seeming) contradiction between the cute fact that (all else being equal) heavier things don’t fall any faster than light things because their extra mass offsets the extra gravitational force upon them, yet in the real world heavier things always fall faster. It’s a bit like this: you earn $1M a year and I earn $100k per year and we both save 10% of our respective earnings per annum. But if our expenses each increase by $11,000 per year, you’re fine, I’m screwed.
We need to look at this from a linguistics perspective as well. By telling the fat kid to “Tell them to go suck it”, the OP was stating that the assertion of the kids on the hill was false. Trying to limit the discussion to gravity ignores this factor that ties in the statements made by other kids. The OP is incorrect.
The acceleration going down the hill is most certainly not proportional to their masses.
That would say that a kid weighing twice as much would accelerate twice as fast. They do not. The difference is small.
You went for an energy arguement. Remember that both potential and kinetic energy are proportional to mass. It’s true that a fat kid has more potential energy at the top, but he takes more kinetic energy to keep going as well.
The differences are small and subtle. Things like “a coefficient of friction isn’t always independent of pressure, it’s just pretty close” and “wind resistance depends on the cross sectional area while mass depends on the volume”. These are things that are typically ignored even in college level introductory courses in mechanics.
Pure 1st year Newtonian mechanics ignoring friction, air resistance, etc., he acceleration will be the same for both. Both will be going the same speed at the bottom of the hill.
But now we can no longer ignore friction as the sleds go forever until they run into an construction. With the same speed at the bottom of the hill, the fat kid has more momentum and more kinetic energy so it takes more force to slow him down to a stop. Unless there’s correspondingly more friction to slow him, he’ll go further.
There’s less friction on the ice, more on a bare street, I’d assume. I dunno on loose snow.
I didn’t say that their acceleration would be proportional to their masses. What I said was “the rate of acceleration of the respective kids downhill is proportional to their respective masses, and the forces on them”.
If you leave out bits of equations, they break and don’t work. Handle them carefully.
What I said, in sentence form, was F=MA. You can argue that is wrong if you like. Good luck. When you succeed, remind me to congratulate you on your Nobel.
I’m not sure why you think I don’t understand this. As I said, the heavier object has more resistance to overcome, but the increase in resistance is marginal while the increase in energy is substantial, which produces the imbalance which results in the heavier object going further.