# Lifting container with low pressure that keeps lid on

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1. Sep 17, 2016

### Vova

1. The problem statement, all variables and given/known data
The question is:

A 2 litre cooking pot (diameter: 20 cm, mass: 300g) is closed with a tight fitting lid, and contains only air. What mass of air can be maximally in the pot so that you can lift the lid, and the pot will move with the lid? Assume the surrounding pressure is p0 = 0.9 bar, and the temperature is 19°C.

2. Relevant equations

pV=mRT
F = Fp + FG

3. The attempt at a solution

I'm stuck on the free body diagram for this question. I'm thinking that if the pressure inside the pot is lower than the outside, the lid will stay on as the pot is lifted (obviously). I think this might be the force equation:

F = Fp + FG

where F = force upwards on lid, Fp = force of lower air pressure inside pulling down on lid, and FG = force down on (mass of pot + mass of air) by gravity.

First of all, I'm not sure if that makes any sense. Does it take extra force upwards to compensate for the force pulling down on the lid due to negative air pressure/force pushing down on the lid by the greater outside pressure? Also, how can I figure out any of the forces if the mass of air is unknown? I just don't know where to start and I can find no relevant examples that explain this.

2. Sep 17, 2016

### andrewkirk

Let C be the container, excluding the lid. To simplify, assume the container is a vertical cylinder and the lid is the whole of the top. What is the net force vector of air pressure on C? To figure that out, consider these sub-questions:

Can we ignore pressure forces on the sides? Why?
What is the net force vector from air pressure on the bottom of C?

Having figured that out, imagine holding the lid so that the container just dangles still and upright in the air. In the light of the answers to the previous sub-questions, what is the maximum weight of C such that it will not fall down?

By the way, the mass of 300g in the question must be the mass excluding the lid, ie the mass of C.

Supplementary question: They have given us the diameter of C. Do we need it? Why/why not?

3. Sep 17, 2016

### Vova

1. The net force of air pressure on the container is pointing inwards? Since the pressure on the inside is lower than the outside?
2. The pressure on the sides of C does not affect its buoyancy in air?
3. The negative pressure inside C means that the force vector points upwards from the bottom, thus making it more buoyant?