Sag and Lift | PhysElo

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7.Sag and Lift

+10

A block of mass

m

hangs from one end of a massless, inextensible string that passes over a massless, frictionless pulley fixed to the ceiling. The other end of the string is fastened to a wall, so that the segment between the pulley and the wall is initially horizontal with length

L

. A small mass

m

, attached to a massless frictionless ring, is now threaded onto this horizontal segment; the system is released and settles into a new equilibrium. Neglecting friction everywhere, by how much has the hanging block risen relative to its original position?

$Show a frictionless pulley fixed to the ceiling near the top left. A string runs over the pulley: on the left it hangs vertically and supports a block labeled $m$; on the right it extends to a fixed point on a wall at the same height as the pulley. Draw the original horizontal segment as a dashed line of length $L$ between the pulley and the wall point. Superimpose the loaded configuration: a symmetric V dipping below the dashed line, with a small ring carrying mass $m$ at the vertex. Label the equal angles $\theta$ between each leg of the V and the horizontal dashed line, and label the horizontal distance $L$ between the pulley and the wall attachment.$

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