Question

Consider a box with a lid 2.1 m wide and 0.62 m long. If the inside of the box is evacuated (i.e., its pressure is zero), how much force is required to open the lid?

Answer 1

I will assume that the lid of the box is rectangular. The total force on the lid is calculated as P*A where P is the pressure difference between the outside and the inside of the box, and A is the area of the lid

A = 2.1*0.62 = 1.302 m^2.

Since the pressure inside the box is zero, P is the pressure outside the box. We are not told what this is, so we cannot answer the question. However, we can say that the total force is 1.302*P

The standard atmospheric pressure is 101.3kPa, so if you assume that P has this value, then P*A evaluates to 131.89 kN

The force required to open the box depends on how the lid is opened. If the lid is hinged down one edge, and the force is applied to the opposite edge, the force required will be P*A/2.

If the lid is not attached to the box at all, and is lifted off by a force applied at its centre (i.e. at the intersection of the diagonals) so that it becomes detached along all edges simultaneously (unlikely in practice), the force will theoretically be P*A.