Evacuatred chamber pressure question

[Kristin]

I've been working on this question for quite a while and I've tried several methods with no success. I am no where near confident in my method and I was wondering if someone could point me in the right direction. The question is:

A 16.5 cm diameter circular cover is placed over a 8.0 cm diameter hole that leads into an evacuated chamer. The pressure in the chamber is 22.5 kPa. How much force is required to pull the cover off?

I attempted to solve by using F1/A1=F2/A2
so... I got F1=P1A1
=113.1N

And 113.1N/5.027e-3m=x/2.138e-2m
Isolating for x, and then F2=481N
I have also tried other methods and gotten F2= 1510N, 156N, 1511N, 212N, and 665N.

 

[mezarashi]

You are nearly right. You have to consider your free body diagram a bit more carefuly. There are 3 forces involved.

1. The atmospheric pressure acting down on the cover. F = PxA.
2. The chamber pressure acting up on the cover. F = PxA
3. The force of you pulling up on the cover.

Solve the diagram for the force of you pulling.

 

[quicknote]

Hello,

First of all, it is great that you have been working on this question and have tried multiple methods. It shows that you are dedicated to finding the correct solution. However, it seems that you are getting different results each time you try a new method. This could be due to a mistake in your calculations or not considering all the necessary factors.

To find the force required to pull the cover off, you need to take into account the atmospheric pressure outside the chamber. This will create a pressure difference between the inside and outside of the chamber, which is what will cause the force needed to pull the cover off.

One way to approach this problem is by using the formula F = PA, where F is the force, P is the pressure, and A is the area. In this case, the area would be the surface area of the cover. So, you would need to calculate the total surface area of the cover (including the area of the hole) and then multiply it by the pressure difference between the inside and outside of the chamber.

Another method you could try is using the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. In this case, you would need to calculate the volume of the chamber and then use the ideal gas law to find the number of moles of gas inside the chamber. From there, you can calculate the force using the formula F = nmg, where m is the mass of the gas and g is the acceleration due to gravity.

It is important to note that both of these methods assume that the cover is perfectly sealed and there is no air leakage. If there is air leakage, the force required to pull the cover off will be different.

I hope this helps point you in the right direction. It is always a good idea to double-check your calculations and make sure you are considering all the necessary factors when solving a problem. Good luck!