Problem2 A cylinder of mass M is floating in a liquid (see diagram). Thecross se

Question

Problem2

A cylinder of mass M is floating in a liquid (see diagram). Thecross sectional area of the cylinder is A and the height of thecylinder is h. A cable is attached to the top of the cylinder,routed across a pulley, and attached to a hanging mass. Initially,the cylinder and mass are at rest. When at rest, the hanging mass(treat as point particle) is at the same height as the surface ofthe liquid (y=0).

If the cylinder is displaced slightly from rest, it begins tomove. Use the coordinate system and variables shown in thediagram.

a.)        What is thesubmerged volume in terms of y and h? The variable y measures thedistance from the bottom of the container to the center of mass ofthe cylinder.

b.)        What is thebuoyant force?

c.)        Draw Free BodyDiagrams for both the cylinder and hanging mass. Compute the netforce on the cylinder.

d.)        Is the motionSimple Harmonic? Why or why not? (prove the assertion with anequation)

Explanation / Answer

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