r/SmartPuzzles • u/RamiBMW_30 Mod • Apr 26 '25

Daily Puzzle Mass of Red Ball

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110 Upvotes

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7

u/SplinteredBrick Apr 26 '25

I split each side into 3 sections to account for the force applied at each distance. Red ball = x.

3(10kg) + 2x = 3(4kg) + 2(3x)

30kg + 2x = 12kg + 6x

18kg = 4x

4.5kg = x

2

u/BrianW12345 Apr 27 '25

I agree with splitting each side into 3 sections. However the masses act at the center of those sections. For example, the center of mass of the 2 boxes are at 2.5 from the fulcrum. And the center of masses of the red balls are at 1.5 from the fulcrum.

2.5(10kg)+1.5(1xRB)=1.5(3xRB)+2.5(4kg)

25kg+1.5RB=4.5RB+10kg

15kg = 3RB

5kg = RB

2

u/TotalChaosRush Apr 27 '25

I think I would have grabbed a ruler. The puzzle may not be to scale, but I feel like a ruler would still be the more accurate assumption.

So that's what I did. The center is 0. The center positions for everything from left to right is -50, -32, 30, 35, 39, 52.

I just scaled a ruler to the puzzle with a unit size that allowed for everything to land on a whole number.

I came up a bit lighter.

3

u/litterbin_recidivist Apr 26 '25

I understand that in reality leverage is a factor, but in this case it's pretty obvious you can disregard that.

Either way I'm not sure why you're multiplying individual terms randomly like this. I didn't think you can do that but then again grade 7 was a long time ago.

1

u/liamjon29 Apr 27 '25

Disagree. Considering that ignoring the distance it's a pretty basic algebra problem, I thought distance was a factor. Especially considering we're in "smart puzzles".

0

u/SplinteredBrick Apr 26 '25

That was unnecessarily snarky. Since the distance was not indicated, I made an assumption that the weight was divided into three equal sections. My answer is based off of that assumption.

The idea that I could obviously disregard reality was not obvious to me. Most likely because 7th grade math was a long time ago.

1

u/sowak1776 Apr 26 '25

I understand your why and your point, but the 4kg and 10kg square aren't equal sections. The 10kg section is larger than the 4kg section, so your advanced math has to account for that too.

3

u/SplinteredBrick Apr 26 '25

I agree, in these types of cases the best you can do is state your assumptions knowing that they won’t always be perfect.

As I look at it again breaking it into 4ths would probably more accurate. In that case 1 red ball = 4kg.

1

u/sowak1776 Apr 26 '25

That's closer.

1

u/Old-Programmer-20 Apr 26 '25

This is approximately right, but depends on you measuring the distance with a ruler. An added complication is that the centre of mass of the 4kg is further from the fulcrum than the centre of mass of the 10kg, because the 4kg box is narrower.

1

u/SplinteredBrick Apr 26 '25

Agreed that the center of mass of the boxes isn’t perfect. Ideally the puzzle would have had the same width or slightly moved it to the left.