Calculate Centre of Mass with Unknown Mass: Ricardo & Carmelita on Canoe

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SUMMARY

In the discussion, Ricardo, weighing 80 kg, and Carmelita, whose mass is unknown, are in a 30 kg canoe. When they exchange seats, which are 3 m apart, the canoe shifts 40 cm relative to a submerged log. By applying the principle of conservation of momentum and the formula for the center of mass (COM), Ricardo calculates Carmelita's mass as 60 kg. The calculations involve setting up equations for the initial and final positions of the COM, factoring in the unknown mass.

PREREQUISITES
  • Understanding of center of mass (COM) calculations
  • Basic principles of physics related to momentum
  • Algebraic manipulation of equations
  • Familiarity with weight distribution in a system
NEXT STEPS
  • Study the principles of conservation of momentum in closed systems
  • Learn about center of mass calculations in multi-body systems
  • Explore real-world applications of COM in physics
  • Investigate the effects of mass distribution on stability in floating objects
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Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of mass distribution in floating systems.

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Ricardoof mass 80Kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30Kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3m apart and symmetrically located with respect to the canoe's centre. Ricardo notices that the canoe moves 40 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

I'm guessing that I should first find The COM of the canoe with the people in it. How can I do this with an unknown second mass?
 
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Lets say the unknown mass is M. write the expression for the center of mass with this variable. Write the expression for the center of mass in the new position. You know that they will be in the same place.
 

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