Question

John’s mass is 98.6 kg, and Barbara’s is 67.0 kg. He is standing on the x axis at xJ = +9.45 m, while she is standing on the x axis at xB = +4.39 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?

Answer 1

Solution :

Given :

m_J = 98.6 kg

m_B = 67 kg

Initially : x_J = 9.45 m and x_B = 4.39 m

let X_i denote intial center of mass :
X_i = (m_J * x_J + m_B * x_B) / (m_J + m_B)
X_i = { (98.6)(9.45) + (67)(4.39) } / (98.6 + 67)
X_i = (931.77 + 294.13) / (165.6)
X_i = 7.403 m

After changing their position :
x_J = 4.39 m and x_B = 9.45 m

Now : let X_f denote intial center of mass :
X_f = (m_J * x_J + m_B * x_B) / (m_J + m_B)
X_f = { (98.6)(4.39) + (67)(9.45) } / (98.6 + 67)
X_f = (432.854 + 633.15) / (165.6)
X_f = 6.437 m

Therefore: distance moved by center of mass = X_i - X_f = 7.403 m - 6.437 m = 0.966 m