Thank you for the opportunity to help you with your question!
(Assuming ideal pulleys) The mass m2 can be increased from very low mass to higher mass until its weight (force) moves the object on the rough table. The force it pulls on the string with is the same force as its weight because it is hanging. The mass m1 has its weight causing the static friction between it and the table. Some proportion of its weight, μ, keeping it from moving. When the string force is greater than the static friction force, the object will move.
(m1)(g)(μ) = (m2)(g) with μ as the unknown and (m1)(g)(μ) is the tension T on the string, pulling the object.Please let me know if you need any clarification. I'm always happy to answer your questions.
Correction: (m2)(g) is the tension on the string. (m1)(g)(μ) is also the tension on the string, but only when the object begins to move.
Content will be erased after question is completed.