A pressure cooker is shaped like a can

with a lid 25 cm in diameter. If the pressure
in the cooker can reach 3.0 atm, how much
force must the latches holding the lid onto the pot be designed to withstand?

I have F=PA
I have my P: 3.03 * 10^3 N/m^2
A=pi(.25 * 10^2m^2)^2

I'm not sure If I am doing it right.

3.0 atm is 3.04*10^5 N/m^2. There is also a pressure of 1 atm on the outside, so the latches only have to withstand a net pressure force of 2 atm = 2.03*10^5 N/m^2.

Your lid area is incorrect also. It is (pi/4)*D^2 = 4.91*10^-2 m^2.

OH! well Thank you! My teacher seems to leave like .. most of that out.. geez!

F=P*A

A= Pi*r^2
A=Pi*(25/2)^2
A=0.04909 cm^2
Pgauge=Pabs- 1 atm
p abs =P gauge+1
P abs= 4 atm
F= (0.04909 cm^2 * (1m^2)/(100cm)^2)*(4 atm*1.013*10^5 N/m^2)
F=1.99 N

You are on the right track! Let's break down the problem step by step.

First, let's calculate the area (A) of the lid. Given that the diameter (d) of the lid is 25 cm, we can find the radius (r) by dividing the diameter by 2:

r = d/2 = 25 cm / 2 = 12.5 cm

Now, let's convert the radius to meters since we want the result in SI units (meters):

r = 12.5 cm * 0.01 m/cm = 0.125 m

Next, we can calculate the area (A) of the lid using the formula for the area of a circle:

A = π * r^2 = π * (0.125 m)^2

Now that we have the area of the lid, we can calculate the force (F) using the formula F = P * A, where P is the pressure in the cooker.

Given that the pressure (P) is 3.0 atm, we need to convert it to SI units (Pascal):

1 atm = 1.01325 × 10^5 Pa

P = 3.0 atm * 1.01325 × 10^5 Pa/atm

Now, substitute the values of P and A into the formula:

F = P * A = (3.0 atm * 1.01325 × 10^5 Pa/atm) * (π * (0.125 m)^2)

Now you can simplify and calculate the force (F).