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## Homework Statement

" A spring of the pressure gauge shown below has a force constant of 1250 N/m , and the piston has a diameter of 1.20 cm. AS the gauge is lowered into the water in a lake, what change in depth causes the piston to move by 0.750 cm? "

## Homework Equations

F = kx

dF = pressure dA

pressure = density * height * gravity

## The Attempt at a Solution

My first concern is my approach at integration the correct method? Is there an easier way?

Well, I know that the force to be applied is : F = xk = 9.375 N and this force is due to the continually increasing pressure as the piston is dropped into the lake.

Thus I need to be evaluating for the upper limit of the integral

Since dF = pressure dA ,

F = ∫ pressure dA

= ∫ ρ * g * h dA

= ∫ ρ * g * (H-y) dA

I get stuck here, I know I need to integrate with respect to y. What is the relationship between dA and dy? Also why are we given the diameter of the piston.

I have attached a copy of my written work.

Any help is really appreciated, thank you for your time.

-Sakonpure6

http://imgur.com/LOU5cKR