In the figure provided, the masses are m₁ = 5 kg and m₂ = 2 kg , while the applied force is F = 1 N . Determine the acceleration of either block. Also, describe the motion of m₁ if the string breaks but the force F continues to act.

Step-by-step solution

Let a be the common acceleration of the blocks and T be the tension in the string. For block m₁ (moving downward), the equation of motion is: m₁ g + F - T = m₁ a For block m₂ (moving upward), the equation of motion is: T - m₂ g - F = m₂ a Adding the two equations, we get: m₁ g - m₂ g = (m₁ + m₂) a a = m₁ - m₂ m₁ + m₂ g Substituting m₁ = 5 kg , m₂ = 2 kg , and taking g = 10 m/s ^2 : a = 5 - 2 5 + 2 10 = 30 7 4.3 m/s ^2 When the string breaks, the tension T becomes zero. The forces acting on m₁ are its weight m₁ g an