" 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? "
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.