Double Atwoods Machine. In Fig. P5.114 masses m1 and m2

Chapter 5, Problem 5.114

(choose chapter or problem)

Double Atwood’s Machine. In Fig. P5.114 masses \(m_1\) and \(m_2\) are connected by a light string A over a light, frictionless pulley B. The axle of pulley B is connected by a light string C over a light, frictionless pulley D to a mass m3 . Pulley D is suspended from the ceiling by an attachment to its axle. The system is released from rest. In terms of \(m_1, m_2, m_3\), and g, what are (a) the acceleration of block \(m_3\); (b) the acceleration of pulley B; (c) the acceleration of block \(m_1\); (d) the acceleration of block \(m_2\); (e) the tension in string A; (f) the tension in string C? (g) What do your expressions give for the special case of \(m_1 = m_2 \) and \(m_3 = m_1 + m_2\)? Is this reasonable?