Evacuatred chamber pressure question

[Kristin]

I've been working on this question for quite a while and I've tried several methods with no success. I am no where near confident in my method and I was wondering if someone could point me in the right direction. The question is:

A 16.5 cm diameter circular cover is placed over a 8.0 cm diameter hole that leads into an evacuated chamer. The pressure in the chamber is 22.5 kPa. How much force is required to pull the cover off?

I attempted to solve by using F1/A1=F2/A2
so... I got F1=P1A1
=113.1N

And 113.1N/5.027e-3m=x/2.138e-2m
Isolating for x, and then F2=481N
I have also tried other methods and gotten F2= 1510N, 156N, 1511N, 212N, and 665N.

 

[mezarashi]

You are nearly right. You have to consider your free body diagram a bit more carefuly. There are 3 forces involved.

1. The atmospheric pressure acting down on the cover. F = PxA.
2. The chamber pressure acting up on the cover. F = PxA
3. The force of you pulling up on the cover.

Solve the diagram for the force of you pulling.