The spring of the pressure gauge shown in the figure at right has a force consta

Question

The spring of the pressure gauge shown in the figure at right has a force constant of 10,000 N/m, and the piston has a cross sectional area of 0.004 m2 . As the gauge is lowered into water in a lake, what would the compression of the spring (from its relaxed position) be when the piston surface is at a depth of 2 m from the water surface? Neglect the weights of the piston and the spring and assume that the pressure in the piston chamber is zero.

Answer is 4.8cm. Please show in detail how to solve.

Explanation / Answer

The pressure needs to be enough to exert a force on the piston of
F = kX = 10000*x
P =10000*x/0.004 N/m^2

Set that equal to (depth)(density)*g and solve for compression in spring x

10000*x/0.004 =2*9.8*1000

x=0.784 cm

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