A cylinder with cross-section area A floats when it is partially submerged (dept

Question

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

(a) Find an expression for the force F needed to push the cylinder 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 by the force F to push the cylinder a
distance x deeper into the water. (Hint: F is not constant, so an integration is required.)
(c) If you push the floating cylinder down and release it, it bobs up and down. So it is like a spring in the sense
that it oscillates if displaced from equilibrium. Use your result from part (a) to determine the restoring
force on the cylinder. (Remember, a restoring force looks like F = -kx.) Determine the

Explanation / Answer

f

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