Physics: Force Calculation for volume?

[Edemardil]

I am done with my homework this week but there is one question that I could not get anywhere with:

A moonshiner makes the error of filling a glass jar to the brim and capping it tightly. The moonshine expands more than the glass when it warms up, in such a way that the volume increases by 0.6% (that is, ΔV/V₀ = 6 ✕ 10^-3) relative to the space available. Calculate the force exerted by the moonshine per square centimeter if the bulk modulus is 1.9 ✕ 10⁹ N/m², assuming the jar does not break.

Answer __________ N/cm² 

^{It later asks if the jar survives which I can figure out on my own but I do not even know where to start with this. I've read the weekly chapters twice now and spent maybe 2 hours on this and I'm just at the limit now. Could someone throw an equations at me or something? I don't want anyone to do it for me but like I said I have no idea even where to start with this. I know that F = m*a and to get pressure we can use P = F/A.}

^{So I have the pressure I guess as} 1.9 ✕ 10⁹ N/m^{2 and I guess I would have to convert that to N/cm^2 which would be 1.9e4 N/cm^2}

^{So 1.9e4 N/cm^2 = F/A}

^{I'm just stuck and would be grateful if anyone could put any insight into this, if not for my homework, for my final at the end. I'm beginning to think this question is in the wrong section because the two chapters I read have nothing to do with this.}

[Sensei]

If you're converting from m^2 to cm^2 you need to divide by 100 twice (because 1 m^2 is 100*100 cm^2 = 10000 cm^2). e.g. 1.9*10^9 N/m^2 is 1.9*10^5 N/cm^2...

 

[Edemardil]

5 minutes ago, Sensei said:

If you're converting from m^2 to cm^2 you need to divide by 100 twice (because 1 m^2 is 100*100 cm^2 = 10000 cm^2). e.g. 1.9*10^9 N/m^2 is 1.9*10^5 N/cm^2...

 

Omg thank you.

I have been going back to this problem for two DAYS and it was as simple as that. You my friend are my hero right now.

 

Here is what I got final btw.

ΔV = (1F)/(BA)*Vo

11.4e6(f) = a * Vo
11.4e6(f/a)=Vo
 ΔV/Vo = 6x10e-3

6x10e-3 = 1F/BA
6x10e-3 = F/(1.9e9 * A)
6e-2 * 190e3 = F/A
1.14e3 = F/A

[studiot]

52 minutes ago, Edemardil said:

You my friend are my hero right now

Give the man a green star then

here I will do it for you.

+1 sensei

[J.C.MacSwell]

19 hours ago, Edemardil said:

 

^{So I have the pressure I guess as} 1.9 ✕ 10⁹ N/m^{2 and I guess I would have to convert that to N/cm^2 which would be 1.9e4 N/cm^2}

^{So 1.9e4 N/cm^2 = F/A}

 

If the volume would expand X% due to temperature, but is constrained not to, the pressure required would be X% of the bulk modulus. 

Reading the question:

In this case it is allowed to expand somewhat, where without constraint it would otherwise have expanded 0.6% more...so the pressure required (pressure of the moonshine and also the pressure on the walls of the glass jar constraining the volume from increasing further) is 0.6% of the bulk modulus. 

Edit: Note that the bulk modulus used in this manner is only accurate for small changes/restrictions in volume.

Edited July 22, 2018 by J.C.MacSwell

[Edemardil]

On 7/21/2018 at 4:10 PM, studiot said:

Give the man a green star then

here I will do it for you.

+1 sensei

I'm new, how do I do that? I gave him a green arrow instead.

[studiot]

That's the same thing.