Question

Pressure cookers have been around for more than 300 years, although their use has greatly declined in recent years (early models had a nasty habit of exploding). How much force must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is 25.0cm in diameter and the gauge pressure inside is 300 atm? Neglect the weight of the lid.

(a) 7.06×10^4 N
(b) 7.85×10^5 N
(c) 7.85×10^3 N
(d) 7.06×10^5 N

Answer 1

The latches holding the lid onto a pressure cooker must be able to withstand a force of 1.50×10^6 N.

Step-by-step explanation:

To determine the force that the latches holding the lid onto a pressure cooker must be able to withstand, we can use the formula for pressure:

Pressure = Force / Area

First, we need to calculate the area of the circular lid:

Area = π * r^2

In this case, the radius (r) of the lid is half of the diameter, so it would be 25.0 cm / 2 = 12.5 cm = 0.125 m. Now we can calculate the area:

Area = π * (0.125 m)^2 = 0.0491 m^2

Next, we can rearrange the formula for pressure to solve for force:

Force = Pressure * Area

Given that the gauge pressure inside the pressure cooker is 300 atm, we can convert this to Pascals by multiplying by 101325 (since 1 atm = 101325 Pa):

Pressure = 300 atm * 101325 Pa/atm = 30,397,500 Pa

Now we can calculate the force:

Force = 30,397,500 Pa * 0.0491 m^2 = 1,496,874.25 N

Rounded to the nearest significant figure, the force must be able to withstand is 1.50×10^6 N.