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/sci/ - Science & Math

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3173312 No.3173312 [Reply] [Original]

Here's a little physics problem I encountered in the bathroom this morning. In our house we have two bathroom scales, from different people moving in and bringing their own.

In the shower I was wondering what would happen if I put one on top of the other and then stood on both of them, so that the top scale was weighing me, and the bottom scale was weighing me plus the top scale. I naively thought that the top scale would only show half my weight, since the springs in the two scales would be sharing the load between them.

However, when I tried it the top scale showed my full weight. I offset the scales about 5 cm so I could read the bottom one too, and they both show my full weight (with the bottom one a little more because of the weight of the top scale). What is the explanation for this? Why isn't the load divided between the two scales?

>> No.3173328

Why would they?

>> No.3173340

They would show half your weight if you stood with one foot on each of them.

It's the same thing as springs in series or parallel.

>> No.3173358

they're both just weighing things.

>> No.3173360

>>3173312
Think about it, if gravitational force was lost by stacking objects, you could put a scale under anything you carry and half the weight would be lost in the tension of the springs. That would be an interesting universe, but is definately not ours.

>> No.3173370
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3173370

F1: your weight
F2: force of top scale on you
F3: force of you on top scale
F4: force of bottom scale on top scale
F5: force of top scale on bottom scale
F6: force of floor on bottom scale

Neither you nor the scales are accelerating, so by F=ma:
F1+F2=0
F3+F4=0
F5+F6=0

Newton's third law says:
F2 = -F3
F4 = -F5

So
F1 = -F2 = F3 = -F4 = F5 = -F6

This is neglecting the weight of the scales, of course.

>> No.3173378

Thats abit counterintuitive.

I suppose they're both supporting (virtually) the same weight so providing the same upward reaction force. But Its not what you'd expect you'd expect. You'd expect half the weight would be "Used up" or absorbed in displacing the first scale but weight doesn't work that way. Thats probably the first thought we all have but when you put it into words it sounds kinda retarded to think lol.

>> No.3173389

Obviously the scale is wrong. You need to adjust it.

>> No.3173396

Look at it from the bottom-most scale's perspective. It "feels" the weight of you plus the other scale. It does not know what's going on up there, all it knows is that something with your combined weight is pressing down on it. It would show the same if you held the second set of scales in your hands. It doesn't matter what the top scale is doing (weighing you).

If the scales indeed showed half your weight, that would mean the lower one is not experiencing the full weight of you. Where would this weight have gone?

>> No.3173409

If the bottom of the spring isn't accelerating, and the top of the spring has your full weight on it, it's going to compress the same amount, whether the bottom of the spring is resting on the floor, a series of other springs, or a vat of marshmellows.

>> No.3173417

>>3173378
>you'd expect you'd expect. You'd expect
stop expecting

>> No.3173470

The way I look at it is that he your weight is absorbed by the fist scale and added to its weight. Now the bottom scale feels the weight of the top scale which ways 200x as much as it used to.

>> No.3173921

>>3173417
You'd expect I would have proof readed you'd expect, but apparently I did not.