Weight amount: if we put two potatoes adjacent to each other "touched" they will increase the total weight

Ryan$

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Jan 25, 2019
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177
Hi guys, there's something confused me a lil about weight and I'm trying to relate to to our real life but don't make sense since in our life we aren't getting the same.
if I have one potato weighted 30grams, so if I put another one potato with the same weight 30grams, then should I get in total 60grams, but in real life we are not getting exactly 60grams , we would get 58 grams or something like that because for instance if we put two potatoes adjacent to each other "touched" they will increase the total weight ....so is math not concrete? or shouldn't I relate what math explain to our real life?!
 

ksdhart2

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Mar 25, 2016
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...if we put two potatoes adjacent to each other "touched" they will increase the total weight...
I don't know what this means, because it's obviously untrue. That's just not how any of this works. If you take any two objects, their weight together will always be the same as the sum of their individual weights. If your scale says otherwise, then it's improperly calibrated or otherwise broken.

You can demonstrate this yourself. Find any two objects around your house. Weigh the first one and write down its weight. Weigh the second one and write down its weight. Then put both objects on the scale as far apart as you possibly can, and weigh them together. This weight reading must be the sum of the two numbers you wrote down. Then move the objects closer together and observe that combined weight does not change.

You can do this as many times as you like, with the objects in whatever positions you like - no matter how close the objects are to one another or how much they touch or overlap, their combined weight will always be the sum of their individual weights. Then if you're still somehow unconvinced and you think maybe it's just a coincidence, a weird property of the two objects you picked, try the experiment again with two different objects.
 

Dr.Peterson

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Nov 12, 2017
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Do you have evidence that potatoes do this? Or are you just asking a hypothetical question?

But the fact is that math applies to abstract models of reality, which are not always exactly valid, but approximate. So the mathematical results have to be checked against experimental results, to refine the theory.

For example, in elementary algebra problems we often assume that the volume of a mixture of two liquids is the sum of the individual volumes. That is not always true, so when the difference is significant, we have to modify our equations. It is not the math that is wrong, but the application.

Likewse, the earth's surface is not flat, so we can't apply Euclidean plane geometry to it for large regions, but have to make adjustments for spherical geometry, or even for the "geoid", depending on our needs.
 

topsquark

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Aug 27, 2012
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311
Hi guys, there's something confused me a lil about weight and I'm trying to relate to to our real life but don't make sense since in our life we aren't getting the same.
if I have one potato weighted 30grams, so if I put another one potato with the same weight 30grams, then should I get in total 60grams, but in real life we are not getting exactly 60grams , we would get 58 grams or something like that because for instance if we put two potatoes adjacent to each other "touched" they will increase the total weight ....so is math not concrete? or shouldn't I relate what math explain to our real life?!
I used to have similar questions. I once did a experiment with a simple circuit. I knew the source potential and the current in the circuit and had to calculate the resistance. I had (as I recall) a potential of 4 V from the source and the current was measured to be 2 A. The resistor was rated at 2 \(\displaystyle \Omega\) but when I measured the resistance I got something like 2.2 \(\displaystyle \Omega\)! It drove me nuts.

The answer, as ksdhart2 mentioned is that scales do not give you exact values. You measure the weight (mass, actually, in this case but no matter) of the first potato and get an answer of 30 g from your scale. But is it actually 30.00000000000.... g? No. The scale simply isn't that accurate. Let's say that your scale has an accuracy up to a gram. So maybe your first potato actually has a weight of 30.4 g. Maybe the second one has a weight of 30.8 g. Then the total weight of the two potatoes is 30.4 g + 30.8 g = 61.2 g. According to the scale you picked up an extra gram from nowhere!

Numbers in Physics can be a bit "malleable" due to (impossible to avoid) limitations in the devices measuring them.

-Dan
 

Dr.Peterson

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Nov 12, 2017
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Yes, rounding error is an interesting possibility here; if the potatoes were both actually 29.5 pounds and the scale rounds to the nearest pound, they would read as 30 pounds each, but together they would be 39 pounds. I can't get the total to read as 38, though, unless the scale reads to the nearest two pounds. This is one reason I asked for the evidence (which should include the tolerance of the scales).

The wording of the question suggests that it is not based on actual experiment ("or something like that"), and the hypothesis that touching increases the weight. I'm hoping to hear back from Ryan$ about the basis of the claim.

The resistor is an interesting example of its own. As I recall, resistors are manufactured almost randomly, and just labeled with the nearest value on a scale designed so that every one they make will fall within, say, 10% of one of the chosen values, and none of them "fail". With 10% tolerance, 2.2Ω would be validly marked as 2Ω (actually vice versa, since the former is a standard value) -- so it's not an error in measurement, but a deliberate tolerance in manufacturing. And adding two resistors together will result in something that might differ by more than a mere rounding error from what would be expected nominally.
 

HallsofIvy

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Jan 27, 2012
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There's no problem with the math but there can be a problem with the scale! Certainly two potatoes together will weigh the sum of there separate weights. It doesn't matter if the two potatoes are touching or even if one is on top of the other. If the scale spring is not perfectly elastic then two potatoes together might "strain" the spring more.
 

HallsofIvy

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Typo: Dr. Peterson wrote "if the potatoes were both actually 29.5 pounds and the scale rounds to the nearest pound, they would read as 30 pounds each, but together they would be 39 pounds." What he meant was that together they would be 2(29.5)= 59 pounds rather than 2(30)= 60.

(Those are pretty big potatoes!)
 

topsquark

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Aug 27, 2012
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You and Dr.Peterson need to re-read the OP. The unit of measurement was g, not lb. ;)
 
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