Question

Ricardo, of mass 75 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 34 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 2.7 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 33 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

Answer 1

The coordinate of center of mass is given by,

x_com (before) = x_com (after)

(m_R x_R + m_B x_B + m_C x_C) / (m_R + m_B + m_C) = (m_R x_R' + m_B x_B' + m_C x_C') / (m_R + m_B + m_C)

m_R (d - 1.35) + m_B d + m_C (d + 1.5) = m_R (d - 0.33 + 1.35) + m_B (d - 0.33) + m_C (d - 0.33 -1.5)

m_R d - (1.35) m_R + m_B d + m_C d + (1.5) m_C = m_R d + (1.02) m_R + m_B d - (0.33) m_B + m_C d - (1.83) m_C

- (1.35) m_R - (1.02) m_R + (1.5) m_C + (1.83) m_C = - (0.33) m_B

- (2.37) m_R + (3.33) m_C = - (0.33) m_B

(3.33) m_C = - (0.33) (34 kg) + (2.37) (75 kg)

m_C = (166.53 kg.m) / (3.33)

m_C = 50 kg