Question

The mass of each pulley of the system is m and the mass of the suspended object A is m_A. Determine the force T necessary for the system to be in equilibrium.

Answer 1

Draw free body diagrams of each pulley and the object A. Each pulley and the object A must be in equilibrium. The weights of the pulleys and object A are W = mg and W_A = m_Ag. The equilibrium equations for the weight A, the lower pulley, second pulley, third pulley, and the top pulley are, respectively B - W_A = 0, 2C - B -W = 0, 2D - C - W = 0, 2T - D - W = 0, and F_S - 2T - W = 0. Begin with the first equation and solve for B, substitute for B in the second equation and solve for C, substitute for C in the third equation and solve for D, and substitute for D in the fourth equation and solve for T, to get T in terms of W and W_A. The result is

or in terms of the masses,

T = g/8 (M_A +7m).