Practical physics questions - Pressure & Uncertainty

[charlottexo]

Hey guys, I have a few questions I would like to ask if that is okay

First off: I was doing an experiment regarding Boyle's Law, and there are some questions that accompany it. I had a syringe filled with gas and I had to add mass on the syringe so that the piston moved down. I had to convert the added mass to force and also record the length of the gas column each time I changed the mass. Then I plotted force against length to prove Boyle's Law. The graph was inversely proportional as expected.

Now, it says - How would you adapt your experiment to investigate pressure greater than the atmospheric pressure. It's not the best worded question ever, but what I'm guessing it is asking is that the atmospheric pressure itself is changed from 1 atm to a value that is greater. How would I adapt my experiment? I was thinking I might have to use a pressure gauge to see how much the new pressure deviates from 1 atm, and take that into account but I'm not sure how I would do that. Can anybody potentially see an answer to this?

TLDR: How to investigate pressure greater than atmospheric pressure in Boyle's Law using masses/syringe of gas.

Second: A question on uncertainties. Say I was given a diameter and a length, and I had to calculate firstly, the volume of this cylinder which is easy enough. Then I had to find the percentage uncertainty in the volume (the uncertainty of L and D were both provided).

Normally you'd just add the percentage uncertainty of L to 2 x the percentage uncertainty of the radius. However this time I am given a diameter and it leads to an interesting question. There are two formulae for volume:

∏ (r^2) x L and ∏ x (D^2 / 4) x L

Constants do not affect compound uncertainty, and for each of those formulae you'd either add the uncertainty of (R + R + L) or (D + D + L). Now this obviously leads to two different answers. Assuming that diameter is given to me as 10 ±0.1mm, that means the uncertainty of the radius is also ±0.1mm. Say the length is given as 30±1mm, if you do the uncertainty calculations you will get two different values.

TLDR: Why is it that you can get different percentage uncertainty answers in a compound uncertainty question by using different versions of what is basically the same formula.

Any help would be much appreciated on either of these two questions.

Thanks guys! :) x

 

[charlottexo]

Guys about that first problem to do with the pressure. I think I may have a solution and I was wondering if you could check it please?

Modify the apparatus to include a pressure gauge and see how far above normal atmospheric pressure it reads with no mass. Find the cross sectional area of the syringe and multiply this by how far above the reading was (in pascals of course). This way, you can see how much extra force is being applied relative to normal atmospheric pressure by this new atmosphere.

Then, any readings you take, you subtract this value of force to take into account this excess atmospheric pressure.

I had a long hard think about it, could someone please check that this is right and answer my uncertainty question? Thank you :)

 

[berkeman]

I'm not sure about the uncertainty questions, but my interpretation of the "higher pressure" configuration would be to turn the syringe upside-down...