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Pressure cookers have been around for more than 300 years, although their use has strongly declined in recent years (early models had a nasty habit of exploding). How much force (in N) must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is 22.0 cm in diameter and the gauge pressure inside is 3.20 atm? Neglect the weight of the lid.

Answer :

First, let's convert the diameter to meters and the pressure to Pascal:

22 cm = 0.22 m

3.2 atm = 3.2 * 101325 Pa = 324240 Pa.

Now, let's find the area of the lid:

[tex]\begin{gathered} A=\frac{\pi d^2}{4}\\ \\ A=\frac{\pi\cdot0.22^2}{4}\\ \\ A=0.03801327\text{ m^^b2} \end{gathered}[/tex]

To find the force, let's use the pressure formula:

[tex]\begin{gathered} P=\frac{F}{A}\\ \\ F=P\cdot A\\ \\ F=324240\cdot0.03801327\\ \\ F=12325.42\text{ N} \end{gathered}[/tex]

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