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A cylinder with a cross-section area A floats with its long axis vertical in a liquid of density p. (1) Pressing down on the cylinder pushes it deeper into the liquid. Find and expression for the force needed to push the cylinder a distance x deeper into the liquid and hold it there. (2) A cylinder with a diameter of 4 cm floats in water. How much work must be done to push the cylinder 10 cm down into the water?

A cylinder with a cross-section area A floats with its long axis vertical in a liquid of density p. (1) Pressing down on the cylinder pushes it deeper into the liquid. Find and expression for the force needed to push the cylinder a distance x deeper into the liquid and hold it there. (2) A cylinder with a diameter of 4 cm floats in water. How much work must be done to push the cylinder 10 cm down into the water?

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A cylinder with a cross-section area A floats with its long axis vertical in a liquid of density p. (1) Pressing down on the cylinder pushes it deeper into the liquid. Find and expression for the force needed to push the cylinder a distance a deeper into the liquid and hold it there. (2) A cylinder with a diameter of 4 cm floats in water. How much work must be done to push the cylinder 10 cm down into the water?
Transcribed Image Text:A cylinder with a cross-section area A floats with its long axis vertical in a liquid of density p. (1) Pressing down on the cylinder pushes it deeper into the liquid. Find and expression for the force needed to push the cylinder a distance a deeper into the liquid and hold it there. (2) A cylinder with a diameter of 4 cm floats in water. How much work must be done to push the cylinder 10 cm down into the water?
Expert Solution
Step 1: Solution to part 1

The expression of the pressure is 

P space equals rho g h

where

rho space i s space t h e space d e n s i t y space g space i s space a c c e l e r a t i o n space d u e space t o space g r a v i t y h space i s space t h e space h e i g h t

since the cylinder is being pushed down a distance  of x 

so the formula of pressure becomes


P space equals rho g x t h e space e x p r e s s i o n space o f space f o r c e space i s space F space equals space P A W h e r e space A space i s space t h e space a r e a F space equals rho g x A s o space t h e space r e q u i r e d space f o r c e space i s space rho g x A


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