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 mustbe done by the force F to push the cylinder a distance x deeperinto the water. (Hint: F is not constant, so an integration isrequired.)

Explanation / Answer

the force is required as the buoyancy force is greater thanweight this extra is due to the extra immersion of a distance x =rho liquid*g*x*A this is the force required to hold it in position b)work required to be done is rho liquid*gAx*x/2 this is obtained by averaging the force ie initial+final/2*distance

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