Ricardo, of mass 80 kg, and Carmelita, who is lighter, are...

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

Key Concepts

Conservation of Center of Mass

In an isolated system where no net external forces are acting, the center of mass remains fixed. This principle is used to analyze situations in which internal movements (such as individuals moving relative to a vehicle or board) cause shifts in the positions of the system's components without altering the overall center of mass. Understanding this concept helps in determining unknown quantities, such as relative masses or displacements, when parts of the system reorganize.

Relative Motion and Mass Distribution

When different masses within a system move relative to each other, the overall displacement of the system can be understood by considering the weighted positions of these masses. Analyzing how the movement of one component affects the position of the center of mass enables one to relate the mass distribution to observable shifts. This concept is crucial when calculating unknown masses or distances in problems involving internal rearrangement without external force influence.

Transcript

00:02 Our question says that we have an individual named nicardo of mass 80 kilograms, and i represent that as m sub r.

00:11 Another individual named carmelita, who is lighter, and they're in joining them.

00:16 In a canoe, that's 30 kilograms.

00:19 I label the canoe, m sub b.

00:22 I do that just to avoid confusion because i'm going to use m sub c to represent carmelita.

00:28 So m sub b, canoe, it's very similar, so i use m sub b to represent the canoe.

00:34 When the canoe is at rest, water, they are going to switch seats.

00:37 And these seats are three meters apart, which i label as l, and symmetrically located with respect to the canoe center.

00:45 So the canoe center is l over two.

00:48 If the canoe moves 40 centimeters horizontal relative to peers post, what is the mass of carmelita? okay.

00:55 So i say that the distance the canoe moves, which i call d, is equal to 40 centimeters or 0 .40 meters.

01:01 I change it into meters, so that way it and the length of the canoe are both in the same units and the units of meters, and we're sticking with si units there.

01:10 Okay, so we're going to let the center amass of the two -person system, and it's assumed to be closer to ricardo because it says he's bigger, be a distance that we're going to call the canoe of length l, right? so we can write that as the mass of ricardo, times l over 2 minus x, right, is equal to the mass of the boat times x plus the mass of carmelita times l over 2 plus x...

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