I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks,
A string with negligible mass passes over a smooth pulley V with a particle A of mass $18kg$ on one end of the string and a pulley ($J$) of negligible mass on the the other end
Another string with negligible mass passes over pulley $J$ and has a particle $K$ of mass $12kg$ on one end and a particle $L$ of mass $9kg$ on the other end.
Show the common acceleration of $A$ and $J$ then show the relative acceleration of $K$ and $L$ to $J$.
So far I have worked out that the tension in the top string is equal to twice the tension in the bottom string. $T-2S=0a$ $$T=2S$$
I then plug this into $18g-T=18a$ to get $18g-2S=18a$
From that equation I get $S=9g-9a$
After that I plug the value of $S$ into the equations for $K$ and $L$ then in the equation for $L$ $g$ is canceled out and I am stuck.