What is the pressure inside a covered cup and how is it created?

[jebuss]

Homework Statement

If i covered the top of a cup with an airtight covering, what would be the pressure just below this covering, and how would it have come about?

 

[Chi Meson]

Why would the pressure be any different from the moment before you covered the cup? Has there been any changes in temperature?

 

[jebuss]

well i sort of suspect it is atmospheric, but i was wondering about the mechanism for the transmission of the force through the paper or whatever it is, since in your P=pgh, you measure from the top of the column you have. is there any deforming of the paper, etc

 

[queenofbabes]

If nothing has happened in the cup then it's just atmospheric pressure.

 

[jebuss]

something has happened, you've covered the top. the atmospheric pressure is caused by the weight of the fluid above it, so when you place a barrier there, that weight is partly taken by the glass itself. its seems like its got to be atmospheric , or the top would cave in, but i don't see how the pressure below it becomes atmospheric

 

[queenofbabes]

You're right : if the interior pressure is less than atmospheric, the top would indeed cave in.

The air above the cup now pushes down on the barrier, but so does the barrier push down on the air within the cup with the exact same pressure. Go draw a diagram and label all forces, and carefully consider Newton's 3rd law, it should become clear now.

 

[jebuss]

if the cup covering was totally rigid, wouldn't it be possible for all the atmospheric force to be support by the cups reaction? in which case, why would the gas inside the cup need to exert atmospheric pressure back on the covering.

 

[queenofbabes]

the cup probably could support the covering on its own, yes, but it doesn't happen precisely because there is air in the cup interior and it exerts a pressure upwards as well.

 

[jebuss]

so the cups reaction is equal to the mass of the covering only?

 

[queenofbabes]

yup.

 

[jebuss]

the reason i asked was i was thinking about the upside down glass of water covered with a coaster or something, and wondering what the pressure of the air in the upturned glass was. i know the usual explanation is the gas expands slightly inside, but before that , is it just atmospheric in there?

 

[queenofbabes]

that's correct too =)