Pulleys & Constraints

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In the system shown, the pulley and string are ideal. If the acceleration of block A (mass m) is a upwards, find the acceleration of block B (mass 2m).

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1. **Ideal String Property**: For an inextensible (ideal) string of length $L$, the rate of change of length is zero.
2. **Constraint Relation**: If block $A$ moves upwards by a distance $x_A$, the string on its side shortens. To keep the total length constant, the string on block $B$'s side must lengthen by exactly $x_A$.
3. **Velocity and Acceleration**: Differentiating once gives $v_A = v_B$. Differentiating again gives $a_A = a_B$.
4. **Conclusion**: If block $A$ has acceleration $a$ upwards, block $B$ must have acceleration $a$ downwards (to maintain tension and string length).

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Pulleys & Constraints

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