Randall D. Knight — Newton's Third Law: Problem Challenge_Problem_58

FIGURE CP7.58 shows three hanging masses connected by massless strings over two massless, frictionless pulleys. a. Find the acceleration constraint for this system. It is a single equation relating \(a_{1y}\), \(a_{2y}\), and \(a_{3y}\). Hint: \(y_A\) isn’t constant. b. Find an expression for the tension in string A. Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns. c. Suppose: \(m_1 = 2.5\text{ kg}\), \(m_2 = 1.5\text{ kg}\), and \(m_3 = 4.0\text{ kg}\). Find the acceleration of each. d. The \(4.0\text{ kg}\) mass would appear to be in equilibrium. Explain why it accelerates.