Assignment:
Consider a system of three particles, each of mass m, whose motions are described by {m_1a_1 = F_12 + F_13, m_2a_2 = F_21 + F_23, m_3a_3 = F_31 + F_32}.
If particles 2 and 3, even though not rigidly bound together, are regarded as forming a composite body of mass 2m located at their mid-point r = (1/2)*(r_2 + r_3), find the equations describing the motion of the two-body system comprising particle 1 and the composite body (2+3).
- What is the force on the composite body due to particle 1?
- Show that the equations above (in {}) agree with m_1a_1 = -m_2a_2.
- When the masses are unequal, what is the correct definition of the position of the composite (2+3) that will make m_1a_1 = - m_2a_2 hold true?