A few bits and bobs questions

Tweej

I have a few loose end questions which I just want to get a few views on.

1. Why do hot water pipes burst more frequently during the winter than cold water pipes?
Volume coefficent of water (at 20 deg but accuracy isn't needed) 207*10^-6
Volume coefficent of PVC 157, or copper, 51.

Since water has a much higher coefficent, surely it shrinks much more when it is chilled as opposed to the pipe which surrounds it? (I know water begins to expand below 4 degrees, but why does this effect hot water pipes more than cold?)

I found this http://scifun.chem.wisc.edu/radio/pipefrez.html but the book I'm reading alluded to the hot vs cold bursting in a chapter about volume coefficents, so I can't help but feel it isn't solely due to super cooling

2. In a Spring system, which, hanging from the roof, goes spring, mass, spring, mass, am I able to use the in series spring formula? Am I able to consider the two masses as one? How would one solve this system? Am I supposed to consider it with energy?

3. http://imgur.com/a6NBi8u
Volume of triangular prism = 1/2 * base * height * thickness
Weight of Ice = 1/2 * base * h * thickness * Pice * g
Upthrust of water = 1/2 * base * d * thickness * Pwater * g

Weight = upthrust if it's floating

h * Pice = d * Pwater
d/h = Pice/Pwater

Where does the square root come into it all?

I'm sorry for the probably obvious questions, and much obliged to anyone who can help me

Evan93

For (3) we have that Pice/Pwater=Vwater/Vice. But since the volume of water displaced by the prism is given by Vwater=1/2*l*k*d and Vice=1/2*l*b*h where k is the base of the immersed prism and b the base of the entire prism.

But d/h=k/b because the triangles are similar and that's where the square root comes from.

For (2) I'd be inclined to split the system up and write out the equations of motion for both of the masses. In the special case where the first mass is much smaller than the bottom one then you can use the series approximation for the effective spring I think. Usually when I've come across these problems you'd make the guess that the the system is in a mode and you'd figure out the frequencies of resonance and the system is solved for that special case. Actually, for such a coupled oscillator system there is a continuous exchange of energy between the two masses when the system isn't in a mode and no exchange when the system is in a mode. The reason we usually find the modes of resonance is because the general motion of the entire system is a superposition of these modes, though it is more complicated than the simple case of when the system is in a mode.

Hope that helps and makes some sort of sense.

SOL

For (1)

I would guess that it is because the hot water has been degassed whereas the cold water has not.

When it comes to the final compressive moments inside the pipe the cold water ice can compress the gas bubbles that are trapped (think about an icecube that is made from tap water) where as the hot water will have far fewer of these bubbles.

This is entirely my own speculation and in no way scientifically tested though.

Also, if you are wondering why I say the hot water is degassed, you can look up gas solubility in water vs temperature...

Tweej

Evan93 wrote: »

For (3) we have that Pice/Pwater=Vwater/Vice. But since the volume of water displaced by the prism is given by Vwater=1/2*l*k*d and Vice=1/2*l*b*h where k is the base of the immersed prism and b the base of the entire prism.

But d/h=k/b because the triangles are similar and that's where the square root comes from.
Hope that helps and makes some sort of sense.

God how did I overlook that the base isn't b for both. Thank you

And I'll take a look at the Springs. Thank you for the help!