Question

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 must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is 25.0 cm in diameter and the gauge pressure inside is 300 atm? Neglect the weight of the lid.

A. 27.8 kN
B. 34.7 kN
C. 41.6 kN
D. 48.5 kN

Answer 1

To calculate the force the latches must withstand, multiply the area of the lid by the gauge pressure in pascals. For a lid 25.0 cm in diameter and a gauge pressure of 300 atm, this results in a force of approximately 1.49 MN, which does not correspond to any of the given options, indicating a potential error in the provided information or choices.

Step-by-step explanation:

To determine the force the latches of a pressure cooker must withstand, we need to calculate the area of the lid and multiply it by the gauge pressure. The diameter of the lid is given as 25.0 cm, which means the radius (r) is 12.5 cm or 0.125 m. The gauge pressure is given as 300 atm, which needs to be converted to pascals (1 atm = 101325 Pa).

The area (A) of the lid is calculated using the formula for the area of a circle (A = πr^2), and the force (F) is then calculated using the formula F = A × gauge pressure.

First, convert gauge pressure to pascals:
300 atm × 101325 Pa/atm = 30397500 Pa.

Next, calculate the area of the lid:
A = π × (0.125 m)^2 ≈ 0.0491 m^2.

Finally, calculate the force required:
F = 0.0491 m^2 × 30397500 Pa ≈ 1490572.5 N or approximately 1.49 MN, which is not listed in the options provided. It seems there might be a mistake since none of the options match this calculation. Ensure to double-check the figures and units provided in the question.