As shown in the figure, a constant force F = m₂ g/2 is exerted on the block of mass m₁ . The surface of the table is smooth, and the string and pulley are light. Determine the acceleration of m₁ .

Step-by-step solution

Let a be the acceleration of the system, assuming m₁ moves towards the right and m₂ moves downwards. Let T be the tension in the string. The equation of motion for mass m₁ in the horizontal direction is: T - F = m₁ a The equation of motion for mass m₂ in the vertical direction is: m₂ g - T = m₂ a Adding the two equations, we get: m₂ g - F = (m₁ + m₂) a Given that the applied force is F = m₂ g 2 , substituting this value yields: m₂ g - m₂ g 2 = (m₁ + m₂) a m₂ g 2 = (m₁ + m₂) a Solving for a , we get: a = m₂ g 2(m₁ +