Serway & Jewett — The Laws of Motion: Problem 25

An object of mass \(m_1\) hangs from a string that passes over a very light fixed pulley \(P_1\) as shown in Figure P5.25. The string connects to a second very light pulley \(P_2\). A second string passes around this pulley with one end attached to a wall and the other to an object of mass \(m_2\) on a frictionless, horizontal table. (a) If \(a_1\) and \(a_2\) are the accelerations of \(m_1\) and \(m_2\), respectively, what is the relation between these accelerations? Find expressions for (b) the tensions in the strings and (c) the accelerations \(a_1\) and \(a_2\) in terms of the masses \(m_1\) and \(m_2\), and \(g\).