Principle of Conservation of Momentum: Calculating Carmelita's Mass

How can we calculate Carmelita's mass using the principle of conservation of momentum?

Given the scenario where Ricardo and Carmelita exchange seats in a canoe, resulting in a horizontal movement of the canoe, how can we determine Carmelita's mass?

Calculating Carmelita's Mass

When Ricardo and Carmelita exchange seats in the canoe, the principle of conservation of momentum can be applied to calculate Carmelita's mass. This principle states that the total momentum of a system remains constant if no external forces act on it.

Initially, the canoe is at rest, so the total momentum is zero. However, during the seat exchange, the canoe moves horizontally relative to a pier post, indicating a change in momentum in the horizontal direction.

We can denote Carmelita's mass as 'm' (in kg) and the horizontal displacement of the canoe as 'd' (in meters). The total mass of the system includes Ricardo's mass (82 kg), the canoe's mass (26 kg), and Carmelita's mass (m).

Using the conservation of momentum principle, we can write the equation:

Initial momentum = Final momentum

0 = (82 kg + 26 kg + m) * 0 + m * v

The distance covered by the canoe during the seat exchange is given as 29 cm (0.29 m). The velocity of the canoe ('v') in the horizontal direction can be calculated using the formula:

v = d / t

Substitute the values to find:

v = 0.29 m / 2.8 m = 0.1036 m/s

Substitute this velocity value into the conservation of momentum equation to solve for Carmelita's mass:

0 = (82 kg + 26 kg + m) * 0 + m * 0.1036 m/s

Solving further results in:

0 = 0 + 0.1036 m * m

0 = 0.1036 m^2

Since the left side of the equation must equal the right side (zero), we can determine that Carmelita's mass is 0.