# Really stupid question about either physics, math or philosophy...

Y’know when your kid asks you something that seems really easy and then you go…errr…gibber gibber gibber…and he calls you on it? Yeah, I need to rebuild some cred here.

Situation: I have a 20 pound toddler. She has a 2 pound backpack. If she wears the backpack, she’s bearing a load of 2 pounds, right? If I then pick her up, I’m bearing 22 pounds (20 pound kidlet + 2 pound backpack), so altogether we’re carrying 24 pounds. But, of course, we aren’t. So “where” did the “extra” 2 pounds come from, and how would you explain to a very bright 14 year old (and dim-witted old me) that there’s no extra weight even though both my toddler and I are each carrying that 2 pound backpack?

This reminds be of that old hotel bill brain teaser, which I never quite grokked either.

Is it any more complicated than explaining you are accounting for the same weight twice?
Hotel Bill Brain Teaser

Hotel Bill
This is a nice nonsense. Each guest paid \$9 because they gave \$30 and they were given back \$3. The manager got \$25 and the difference (\$2) has the bellboy. So it is nonsense to add the \$2 to the \$27, since the bellboy kept the \$2.

When the toddler stands on the ground with the 2 lb. pack, the weight of the pack is carried through her spine down to her legs and down to the ground which pushes back by the 2 lb in addition to pushing back with her weight.

When you hold her the 2 lb. is carried through her spine to your arms, your spine and legs down to the ground which pushes back with 2 lb. In both cases the extra force exerted on the ground because of the backpack is 2 lb.

Thank you! I think this will work. It’s what I was trying to say, but he kept catching me up with, “But she’s still holding 2 pounds and you’re holding 2 pounds, so why isn’t it 4 pounds?” And I got confused on what is, admittedly, a very stupid question. We both knew it couldn’t really be 4 pounds, but neither of us could explain WHY that was.

Sometimes I think I wish I had one of those kids who didn’t want to know why and would just accept “because” as an answer! But then I remember how irritating gullible people are and I’m glad he isn’t one.

I am not sure if I am following the complication. Imagine that your toddler weighs 20 pounds. She has a cup with 1 pound of juice in it that she is holding making her weigh 21 pounds in total. She drinks the entire cup. None of the system has changed. Her feet are still holding up 21 pounds.

You pick her up. It doesn’t matter whether the liquid is in her belly or in a cup in her hands. The whole system still weighs 21 pounds.

The question became: so what is she holding, then? If you carry something on, say, an elevator, you don’t feel as if that weight in your arms goes away simply because the elevator is carrying you and your load. Holding a 25 pound bag of cat litter is still tiring, even if someone or something else were to carry you and it.

But everything in that system is carrying the same load. The bag of cat litter is being carried downward first by your arms, then by your feet, then by the elevator, then by the building’s foundation, then by the earth itself. You can’t pick out some part in the middle and say that is the part carrying the load solo. It doesn’t work that way.

You are only bearing 22 pounds. Two of those pounds are exerted on both of you but the total load is still only 22 pounds. There is no “24 lbs.” There is a common load of two lbs, but that common load is not “shared” in the sense that you are both simultaneously taking a portion of it. It goes through both of you sequentially. First it goes through her, then it goes through you. You both bear that full two lbs load but you bear it at different “times,” so to speak.

Try this: Take three blocks, and stack them in a tower. Which one is holding the top block up? If you knock away the middle block, the top block will fall, but if you knock away the bottom block, that’ll make the top block fall, too. So both of those blocks are holding up the same top block.

OK, assume I weigh 175 lbs and have a bag of cat litter weighing 25 lbs.
I understand that the total mass is 200 lbs.

But if I hold the bag in my arms, I get tired.
If I carry it balanced on my head, I get uncomfortable.
If I stand on it, I don’t.

Over to you!

I think the point you’re missing is to consider whether or not there’s any sharing going on.

If two people are supporting different sides of that bag, then it is not very difficult for either of them, because each is holding up only half of what the bag weighs. But if I hold up someone who is holding up the entire bag, then there is no sharing, so it will be just as difficult for me, regardless of whether
[ul]that person is holding the bag in his hand[/ul]
[ul]or if the bag is resting on his lap while I hold him[/ul]
[ul]or if he is on top of the bag while I hold both.[/ul]
In any of those cases, there is no sharing going on, so they are all equally difficult for me.

And if you knock out the floor beneath the blocks, they’ll all fall!

So you have 200 lbs of parakeets on a plane that can only lift 100 lbs. If you can keep 1/2 the parakeets flying you should be OK

What is she holding? A kid just drank a pound of juice! What do you think she is holding?

If you have a plane that can only lift 100lbs, time to get a new plane. This one’s not airtight, anyway!

How does it also support you, the bird-perturbing pilot?

Bzzzzzt!!!

And to answer the OP: The thing is, when the toddler stands on her own on the floor, she exerts the 22 pounds of force on the floor. If we posit her standing on the ground floor, the force is exerted on the Earth.

Now, when you pick up said toddler, she’s still exerting 22 pounds of force downwards; however she is not exerting said force on the Earth but on you. And you, in turn, exert both your own weight and the toddler’s weight and the backpack’s weight on the Earth.

24 lbs? No you’re not. Why would you even think so?

The fact that the 2lb backpack can be separated from the toddler, and is being borne by the toddler, is irrelevant. She is not carrying 2 lbs that are different from and in addition to the extra 2 lbs of the backpack that you carry when you pick her up - it’s the same 2 lbs. Suppose the toddler is standing on the backpack, and you pick them both up that way. Now you’re holding the same 22 lbs, and she’s holding none. Whether she’s carrying it, standing on it, or riding inside of it has no bearing on the matter.

To elaborate - toddler stands on pack, you pick up 22 lbs, toddler bears 0 lbs. Toddler then takes pack from under her and holds it up. Now she bears 2 lbs that she didn’t bear before. But neither she nor pack increased in weight by 2 lbs from her doing that. Her bearing the weight - or not - is irrelevant to what YOU are bearing.

I have a comment about them pigeons. Is this the place to post it?

Jetliners do have a big open window during flight. The cabin is pressurized but not airtight. So I guess flying pigeons would decrease the weight of the plane.

Will this reach the almighty ears, or do I need to post this elsewhere?