Piston Question: Have solution, don't understand rationale

[hanag]

Homework Statement

The drawing below shows a hydraulic chamber in which a spring (spring constant = 1580 N/m) is attached to the input piston (A1 = 15.3 cm2), and a rock of mass 41.9 kg rests on the output plunger (A2 = 66.6 cm2). The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position?

Homework Equations

F1/A1=F2/A2
F=kx

The Attempt at a Solution

F1/15.3 cm^2= 410.62 N/66.6 cm^2 F1=94.33 N

94.33 N= 1580 N/m
0.0597 m

I'm pretty sure this is the correct solution, I just don't understand why I should use F=kx rather than F=kx^2.

 

[berkeman]

Homework Statement

The drawing below shows a hydraulic chamber in which a spring (spring constant = 1580 N/m) is attached to the input piston (A1 = 15.3 cm2), and a rock of mass 41.9 kg rests on the output plunger (A2 = 66.6 cm2). The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position?

Homework Equations

F1/A1=F2/A2
F=kx

The Attempt at a Solution

F1/15.3 cm^2= 410.62 N/66.6 cm^2 F1=94.33 N

94.33 N= 1580 N/m
0.0597 m

I'm pretty sure this is the correct solution, I just don't understand why I should use F=kx rather than F=kx^2.

It looks like you are confusing the equation for spring force (F=-kx) with potential energy stored in a spring (E=1/2kx^2) :-)

http://en.wikipedia.org/wiki/Spring_(device)

http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html

.

 

[hanag]

Oh, I sure was. Thank you so much!