If the blocks A and B are moving towards each | vedclass

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(A) Let the lengths of the string segments be $l_1, l_2, l_3, l_4$. The total length of the string $L = l_1 + l_2 + l_3 + l_4$ is constant,so $\frac{d

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$a \hat{i} - 2(a+b) \hat{j}$

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(A) Let the lengths of the string segments be $l_1, l_2, l_3, l_4$. The total length of the string $L = l_1 + l_2 + l_3 + l_4$ is constant,so $\frac{d^2L}{dt^2} = 0$.From the geometry,the segments $l_1$ and $l_4$ are connected to the blocks. As block $A$ moves right with acceleration $a$ and block $B$ moves left with acceleration $b$,the rate of change of length for the segments is determined by the relative motion.Considering the vertical motion of block $C$ with acceleration $c$ downwards,the constraint equation is $(-a-b) + 0 + (-a-b) + c = 0$.Solving for $c$,we get $c = 2a + 2b$.Block $C$ also moves horizontally with block $A$ with acceleration $a$ in the $\hat{i}$ direction. Thus,the net acceleration of block $C$ is $\vec{a}_C = a \hat{i} - 2(a+b) \hat{j}$.

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ respectively,find the net acceleration of block $C$.

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