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

[suspenc3]

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?

 

[dx]

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.

 

[quicknote]

To calculate the center of mass of the canoe with Ricardo and Carmelita in it, we can use the formula:

COM = (m1x1 + m2x2) / (m1 + m2)

Where m1 and m2 are the masses of Ricardo and Carmelita respectively, and x1 and x2 are their respective distances from the center of the canoe.

Since we know Ricardo's mass (m1 = 80kg) and the distance between the seats (x1 = 3m), we can plug these values into the formula to find the center of mass of the canoe with only Ricardo in it.

COM = (80kg * 3m) / (80kg + m2)

Next, we can use the information about the canoe's movement during the seat exchange to find the new center of mass with both Ricardo and Carmelita in it.

The canoe moves 40cm (or 0.4m) relative to the submerged log, which means that the center of mass shifted by 0.4m as well.

Using the same formula as before, but now with the new center of mass (x1 = 0.4m) and the unknown mass of Carmelita (m2), we can solve for m2.

COM = (80kg * 3m + m2 * 0.4m) / (80kg + m2)

Solving for m2, we get m2 = 10kg.

Therefore, Carmelita's mass is 10kg.