Find the x Coordinate of the Center of Mass of 3 Chocolate Blocks

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To find the x-coordinate of the center of mass for three chocolate blocks with given masses and coordinates, the formula used is (mass1*x1 + mass2*x2 + mass3*x3) / (m1 + m2 + m3). Initial calculations yielded results of 0.051 and 0.05, which were deemed incorrect. After recalculating and ensuring no mistakes were made in the input, the correct x-coordinate was determined to be approximately 0.055543. The final answer was confirmed to be accurate after checking calculations on different devices. The discussion highlights the importance of careful calculation and verification in solving physics problems.
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Homework Statement



Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates:
(1) 0.310 kg, ( 0.200 m, 0.310 m);
(2) 0.410 kg, ( 0.110 m, -0.380 m);
(3) 0.200 kg, ( -0.280 m, 0.610 m).

Find the x coordinate of the center of mass of the system of three chocolate blocks.

The Attempt at a Solution



This is how I commenced,

I took (mass1*x1+mass2*x2+mass3*x3)/(m1+m2+m3) and got .051

this should be right but I got it wrong. I then redid the calculation and this time I got .05
not that much difference, I only got one try left, and don't think this is right because they are so close together.

I did the y the same way and got it right. :S

Please and thank you.
 
Last edited:
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Well, then you have put in the wrong numbers somewhere (I assume that even though you have written m3*x2, that should read m3*x3)
It is impossible for us to know how you clicked about on your calculator.

You should, at least, calculate the following:
\frac{0.310*0.200+0.410*0.110-0.2*0.28}{0.92}=\frac{0.062+0.0451-0.056}{0.92}=\frac{0.0457}{0.92}
which ought to be about what you've found already..
 
Last edited:
for some reason, either my calculator is wack, for the numerator I keep on getting

.062+.0451-.056 = .0511

for the denominator I get .92

.0511/.92 = .055543478

:cry:

edit: I tried it on windows, and I get .0511 too. :O
 
for your x i got .055543. try that and see if it works. I did it how you had it up there and that is what I got. I did this on my homework yesterday and got it right so it should be right. :)
 
yep, it's right thanks. I it just as it showed in the calculator this time without any rounding. :)

thank you princessfrost and arildno for your help.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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