Calculating Mass in a Canoe Swap: A Physics Problem

[Fermat]

...
*im pretty sure that the centre of mass of ricardo+carmelita+canoe does not change when they switch places

The "group" centre of mass does change.
Have you got a ruler handy. Balance it on your finger with two unequal weights (an eraser and a pencil ??) equidistant from the centre. Your finger will be at the COM of the ruler plus two weights. Now switch the positions of those weights. To keep it balanced, your finger will have to move position, so the COM of the "group" has changed.
The total movement of your finger will be twice the distance of it from the mid-point of the ruler.

Edit: could you say where you measured the COM from in each case ?

 

[suspenc3]

I just found this...What do make of it?

http://www.physics.ucc.ie/py1052_ps6.pdf

Q6

 

[suspenc3]

now that I think of it...Their answer makes no sence.

Why would The COM be in the center when the two masses are unequal?

 

[Fermat]

It's a question on conservation of momentum (and energy change). The OP question isn't.

Was there some bit in particular you meant

 

[Fermat]

Ah, you meant Q5.

 

[suspenc3]

are they wrong?

 

[Fermat]

I would say, that solution is wrong!

They say that X is the position of the "group" COM, measured from the centre of the canoe.
Yet they mark it as being equidistant, 3.0m from M and m, even though thay also say it should be nearer to Cian.

Also, they give their eqns as,

X = M(-3.0m) + m_c(0) + m(+3.0m)

But X is a distance, not a moment arm. They forgot to multiply X by the combined mass. M_T = M + m_c + m.

Even if you do that, if you substitute their answer of 68 kg back into those eqns, I got X = -0.202 from the 1st eqn and X = -0.209 from the 2nd eqn.

That last bit makes me believe that, yes, their answer is wrong.

 

[Fermat]

Correction:
They are not (totally) wrong!
The actual answer is m = 68.125 kg

Putting M_T = 178.125 and using m = 68.125kg gives X = -0.2 (I only checked one eqn) I expect the other eqn wiil give the same result.
But it shows that the COM, X, is half the distance moved by the canoe. Which corresponds with my explanation of things