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[KaminaSquirtle]

Ummm, the cubic formula is awfully ugly, so good luck with that.
Unfortunately, I can't help right now, I haven't done this problem before.  But I'll see what I can think of.

[Jim Groovester]

Mega spoilers if you want to figure it out on your own.

It looks like a serious pain in the ass.

[KaminaSquirtle]

Mega spoilers if you want to figure it out on your own.

It looks like a serious pain in the ass.

Yep, you have to make specific substitutions.  Without know what they are beforehand, this will take forever.

[Argembarger]

Well if nobody else has insight into my problem, I guess there's nothing to do but e-mail the professor about it.

Also, screw cubic equations. And quartics and quintics too.

[Virex]

There is no cubic version of the quadratic formula, sorry to burst your bubble.


Anyway, the work done is proportional to the mass displaced and the distance over which you have to displace the mass is also proportional to the mass displaced (since the water level drops). This means it should be pretty trivial to find the solution (pun not intended)

[Argembarger]

The question wasn't so much "how do I go about solving this problem" so much as "I solved this problem, I'm pretty sure it's correct, but the system is telling me I'm wrong, any idea where I went wrong"

And since a couple of people who seem to know what they're doing have told me that my solution appears correct, I am going to investigate the possibility that the system itself is actually wrong on this one (it's extremely rare but not unheard of)

Unless you see where I went off; because I'm getting pretty tired of going over this problem and I need to get moving to finish the rest of them

[dragnar]

There is no cubic version of the quadratic formula, sorry to burst your bubble.

Yes there is... it just isn't usually discussed because it's more of a pain to use than just solving the equation normally.

[RedWarrior0]

There is no cubic version of the quadratic formula, sorry to burst your bubble.

The link posted by JG says otherwise...

And oh, fuck, the link says it looks like the equilvalent of a 12" diameter steel pole covered in pure capsaicin shoved into orifices that are best left unmentioned.

[Jim Groovester]

I did say it looked like a pain in the ass.

[RedWarrior0]

Wrong orifice, bub.


Oh wow did I just type that? Someone needs to bring that to the out of context thread.

Anyways, thanks for the link. It... Helped, I suppose you could say.

[KaminaSquirtle]

Wrong orifice, bub.

Sigged.

[Vector]

There is no cubic version of the quadratic formula, sorry to burst your bubble.

I believe you're thinking of the quintic... and yeah, doodabuddy, don't even try on the quintic, because it just doesn't work.

[RedWarrior0]

Wrong orifice, bub.

Sigged.

Well, on one hand it's my first sig, but on the other hand, it had to be that.

[Wyrm]

Argembarger, I worked out the leaky bucket in well problem myself, and I got somewhere ~1e4 ft·lb of energy (I'm not doing your homework for you). I think I have your error. Your integral should be of the form

W = ∫ F(l)·dl

Instead you have something like this

W ≠ ∫ F(l)·(l(l) dl)

This is wrong, wrong, wrong. Once you get the force as a function of height, you are halfway there.

Edit: in particlar, when the bucket is empty, the work done on the bucket should be a linear function of height. Is the antiderivitive of your second integral (where the bucket is empty) linear?

[Vector]

You, sirrah, are a very, very helpful person who makes me ashamed of my dearth of physics knowledge.  Thank you.