Under Pressure Finding the height of compressed air

[IslandHead]

Homework Statement

A 1.0--tall cylinder contains air at a pressure of 1 . A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. Find the height of the compressed air. It recommends P1V1=P2V2 and that temperature is constant.

Homework Equations

P1V1=P2V2
F=mg
P=F/A

The Attempt at a Solution

P1V1=P2V2
P1A1m=P2hA
(P1*1M)/h=P2

The system is at rest so the force gravity is pulling on the Hg is balanced by the air pressure
PA=F=mg
A(P1*1M)/h=ρ(1-h)Ag
(P1*1M)/pg=h(1-h)
.76=-h^2 + h
0=-h^2 +h -.76
The answers is 76cm ( think the book is wrong) and that quadratic has answers with i in it. I'm unsure what I'm doing wrong! I asked my prof and he couldn't help me. I asked my lab instructor and he says what I did looked right. So 3 people (including me) have missed what is wrong with my work. Please help me :'(

 

[IslandHead]

Am I on the right track for this?

 

[I like Serena]

Welcome to PF, IslandHead!

I believe you are forgetting that the outside force is not just the weight of the mercury, but also the atmospheric pressure.

 

[IslandHead]

so then it will be:

A(P1*1M)/h = 101300A + ρ(1-h)Ag

I'll try solving this

 

[IslandHead]

It works :D i got thanks!

 

[I like Serena]

Cheers!