2 masses and 2 pulleys (Kleppner and Kolenkow)

[AspiringPhysicist12]

Homework Statement

Masses M1 and M2 are connected to a system of strings and pulleys as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. Find the acceleration of M1.

Relevant Equations

x_1 + L_1 + L'_1 + (x_2 + L_2 + L'_2)/2 = constant C

For the official answer, I would appreciate an explanation as to why there's a division by 2 in the constraint equation for the total length of the strings, and why the way I wrote my constraint equation is incorrect.

 

[TSny]

For the official answer, I would appreciate an explanation as to why there's a division by 2 in the constraint equation for the total length of the strings,

Their constraint equation does not represent the total length of the strings. But it does represent a certain fixed quantity. Try to identify what it represents.

 

[TSny]

When you took the time derivative of the first equation, did you treat $a$ as a constant?