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A cylinder with cross-section area A floats with its long
Chapter 15, Problem 49P(choose chapter or problem)
Problem 49P
A cylinder with cross-section area A floats with its long axis vertical in a liquid of density ρ.
a. Pressing down on the cylinder pushes it deeper into the liquid. Find an expression for the force needed to push the cylinder distance x deeper into the liquid and hold it there.
b. A 4.0-cm-diameter cylinder floats in water. How much work must be done to push the cylinder 10 cm deeper into the water?
Hint: An integration is required.
Questions & Answers
QUESTION:
Problem 49P
A cylinder with cross-section area A floats with its long axis vertical in a liquid of density ρ.
a. Pressing down on the cylinder pushes it deeper into the liquid. Find an expression for the force needed to push the cylinder distance x deeper into the liquid and hold it there.
b. A 4.0-cm-diameter cylinder floats in water. How much work must be done to push the cylinder 10 cm deeper into the water?
Hint: An integration is required.
ANSWER:
Step 1 of 2
Part a
We are needed to find the force that would be required to push the cylinder to the given depth.
The force here, would balance the buoyant force that would act on the cylinder in a direction opposite to the applied force.
The area of cross-section of the cylinder is . It is pushed by a distance of
. Therefore, the change in its volume is
.
The density of the liquid is .
Therefore, the buoyant force exerted by the liquid will be .
Therefore, the force concerned should be .