# System of three particles

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?

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#### Solution Preview

Consider a system of three particles, each of mass m, whose motions are described by {m1a1 = F12 + F13, m2a2 = F21 + F23, m3a3 = F31 + F32}.

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)*(r2 + r3), 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 m1a1 = -m2a2.

When the masses are unequal, what is the correct definition of the position of the composite (2+3) that will make m1a1 = -m2a2 hold true?

y 3 F32

F31 F23 2

F21 ...

#### Solution Summary

The expert examines the systems of three particles. A step by step solution provided.