Question

Problem 2. Consider two objects with mi m2 connected by a light string that passes over a pulley having a moment of inertia of/ about its axis of rotation as shown in the figure below. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this instant. in 2h Mo

Answer 1

Given that: - Consider two objects with m_1 > m_2 connected By a light string that passes over a pulley a moment of inertia. (a) Take two objects pulley and Earth as the system if we neglect friction in the system Mechanical Energy is conserved Delta k = k_f - k_i = 1/2 m_1 v^2 + y_2 m_2 v^2 + 1/2 + w^2 v = Rw Delta = 1/2 [m_1 + m_2 + 1/R_2]v^2 Form law of conservation of Energy Delta k + Delta v = 0 1/2 (m_1 + m_2 + 1/R^2) v^2 + m_2 gh - m_1 gh - m_1 gh = 0 v = squareroot 2 (m_1 - m_2) gh/m_1 + m_2 + 1/R^2 (b) v = Rw the angular speed of the pulley at this instant is W = v/R = squareroot 2 (m_1 - m_2) gh/m_1 R^2 + m_2 R^2 + R