Maximum Lift

MediumdynamicsPractice ProblemsSolved by 1

A massless inextensible string runs over a massless frictionless pulley. One end is attached to a block of mass

m

that hangs vertically. The other end is fixed to a wall so that the segment between the pulley and the wall is horizontal and has length

L

. A second mass

m

is attached to the string at the midpoint of this horizontal segment and held there, keeping the string taut and straight. The second mass is then released from rest. Neglect any losses. What is the maximum height the block rises above its initial position during the subsequent motion?

$A pulley at the top center. From the pulley, the string runs horizontally to the right a distance $L$ to a small filled square labeled "wall fixed point." A small mass labeled $m$ is shown at the midpoint of this horizontal segment, with a small hand-symbol or "held" annotation indicating it is held at rest in the horizontal plane (so the string is straight and horizontal). From the pulley, the string also runs vertically downward to a block labeled mass $m$. Label the horizontal segment's full length as $L$ and the midpoint mass with its weight arrow $mg$ pointing down. A small inset or dashed overlay shows the displaced configuration: the midpoint sagged downward by $y$, forming two string segments at angle $\theta$ below horizontal, with the block raised by $z$ on the left side; label $y$, $z$, and $\theta$ on the inset.$

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