Acylinder with cross-section area A floats when it is partiallysubmerged (depth

Question

Acylinder with cross-section area A floats when it is partiallysubmerged (depth h) in a liquid of density liq, as shown onthe left in the figure. Pressing down on the cylinder pushes itdeeper into the liquid.

(a) Find an expression for the force F needed to push thecylinder a distance x deeper into the liquid and hold it there.Your answer may contain some or all of the variables A, x,liq, and any necessary constants.

(b)Determine an expression for the amount of work that must be done bythe force F to push the cylinder a distance x deeper into thewater. (Hint: F is not constant, so an integration isrequired.)

Explanation / Answer

the force needed: F=liq*A*x*g   N work done: F(x)dx=liq*A*g*x2/2

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