pressure cookers have been around for more than 30 years, although their use has stongly declined in recent years.how much force must the latches holding the lid onto pressure cooker be able to withstand if the circular lid is 25 cm in diameter and the gauge pressure inside is 300 atm, neglect the weight of the lid
To calculate the amount of force the latches holding the lid onto a pressure cooker must be able to withstand, we can use the formula for pressure:
Pressure = Force / Area
Here, the pressure inside the pressure cooker is given as 300 atm. However, we need to convert this to a standard unit of pressure, such as pascals (Pa). 1 atm is equal to 101,325 Pa.
Therefore, the pressure inside the pressure cooker is:
300 atm * 101,325 Pa/atm = 30,397,500 Pa
Now, let's calculate the area of the circular lid using the formula for the area of a circle:
Area = π * (radius)^2
Given that the diameter of the circular lid is 25 cm, the radius is half of the diameter, which is 12.5 cm or 0.125 m (converting to meters).
Area = π * (0.125 m)^2
Area = 0.0490874 m²
Now, rearranging the formula for pressure, we can find the force required:
Force = Pressure * Area
Force = 30,397,500 Pa * 0.0490874 m²
Force ≈ 1,493,483.044 N
Therefore, the latches holding the lid onto the pressure cooker must be able to withstand a force of approximately 1,493,483.044 Newtons.