Ricardo of mass 80 kg and Carmelita


Ricardo, of mass 80 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the canoe’s center. If the canoe moves 40 cm horizontally relative to a pier post, what is Carmelita’s mass?

Solution:

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Let L represent the length of the canoe. Let the mass of the canoe be represented by M_{canoe} and the distance from the center of the canoe to the center of mass of the two people be represented by x. The mass of Ricardo is M_R and mass of Carmelita is M_C.

Using these variables, we can write the following:

M_R(\dfrac{{L}}{2}-x)=M_{canoe}x+M_C(\dfrac{{L}}{2}+x)

When they switch positions, we know that the canoe moves 2 times the distance from it’s initial position. Using this fact, we can figure out the value of x.

x=40/2=20\,\text{cm}=0.2 m

 

We can now substitute all the values given to us in the question and solve for M_C.

M_C=\dfrac{{M_R(\dfrac{{L}}{2}-x})-(M_{canoe})(x)}{\dfrac{{L}}{2}+x}

M_C=\dfrac{{(80)(3/2-0.2)}-(30)(0.2)}{(3/2)+0.2}

M_C=57.64 kg

 

Final Answer:

Carmelita has a mass of 57.64 kg.

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