Hello there, I'm trying to understand how Pulleys work. The question asked me to calculate the acceleration constraint that relates the accelerations for each of the masses $m_1, m_2, m_3$. The two ropes are rope $A$ and $B$. The math I did is as follows:
Derivate twice: $$L_B = y_A + y_3$$ $$a_A = -a_3$$ Derivate twice: $$L_A = 2y_A - y_1 - y_2$$ $$2a_A = a_1 + a_2$$ Substitute: $$2(-a_3) = a_1 + a_2$$
This is the correct answer, I'm simply following the method that my professor told us to follow, however this does not make much intuitive sense for me. I just used the lengths provided by the graph. I understand that the tension of Rope A is twice of Rope B, but that didn't help much at all.
How is the acceleration constraint affected by the pulley system? If someone could point me in the right direction or give me resources I'd appreciate it.