The number of kg needed to pull apart Magdeburg Hemispheres

[ShelbyMcD]

Homework Statement

Find the number of kilograms needed to pull apart evacuated Magdeburg Hemispheres whose radii are 25.0 cm when the barometer reads 760mm of Hg.
I really don't know where to start. Could someone walk me through it?

Homework Equations

Unknown.

The Attempt at a Solution

I read somewhere that an equation to help is F=pi*r^2, so I made 25.0cm into 0.250m, and made F=pi*0.0625... but that doesn't seem right.

 

[tiny-tim]

Welcome to PF!

Hi ShelbyMcD! Welcome to PF!

I read somewhere that an equation to help is F=pi*r^2 …

nooo …

how can a force equal an area? ​

 

[ShelbyMcD]

Thank you! Well, that's why I came here... because none of this added up to me haha. Do you know how to help?

 

[tiny-tim]

you want the force, but all you know is the pressure and the area …

what equations do you know that might help? ​

 

[ShelbyMcD]

F=ma? But I don't know the mass. Or maybe P=F/A. But I already have the pressure, which is 760mm of Hg.

 

[tiny-tim]

P = F/A should do it

 

[ShelbyMcD]

So P=F/A, and I only have the radii of the hemispheres... do I use that to find the area of one hemisphere or both and add them together?

 

[tiny-tim]

what do you think?

how are you going to pull them apart … where will the forces be applied?

 

[ShelbyMcD]

On each separate one, in order to pull them apart. So I find the area of one and apply it to the equation?

 

[tiny-tim]

that's right …

you need two forces, a force T on the left, and a force T on the right, and each T has to equal the atmospheric force on that side

(and now I'm off to bed :zzz:)

 

[ShelbyMcD]

Thank you so much for the help! Good night :)

 

[cepheid]

The reason why the hemispheres are hard to open is because they have a vacuum (zero pressure) inside, and there is tons of pressure from the atmosphere outside. We say that a vacuum "sucks" or "pulls", but what's really happening is that the air on the outside of the hemispheres is trying to push them closed, and there's nothing inside the hemispheres to fight back.

So now that you know that it is the air pressure pushing on the spheres that you have to fight against when you pull them open, it should be clear to you *over what area* this pressure acts, and therefore what the force is, right?

 

[Chestermiller]

The reason why the hemispheres are hard to open is because they have a vacuum (zero pressure) inside, and there is tons of pressure from the atmosphere outside. We say that a vacuum "sucks" or "pulls", but what's really happening is that the air on the outside of the hemispheres is trying to push them closed, and there's nothing inside the hemispheres to fight back.

So now that you know that it is the air pressure pushing on the spheres that you have to fight against when you pull them open, it should be clear to you *over what area* this pressure acts, and therefore what the force is, right?

You need to draw a free body diagram on one of the hemispheres, and show the forces acting on it. Then you need to perform a force balance on that hemisphere for the case in which the two hemispheres are just about to lose contact with one another.