i suck! (1 Viewer)

[jessum]

omg. im doing some last minute prep for the trials tomorrow, and i thought i was pretty prepared, did a fair bit of study in the holidays and such, and now im trying to do an hsc paper.. and its taken me 3 hours to get to question 5 and ive only done half the stuff coz i cant do it!! eek
if anyone could give me a basic overview of how to do volumes by slicing, it would be very much appreciated.. because for some strange reason all my knowledge of the topic has totally disappeared.
does anyone else feel that way too? or am i the only one who feels that overnight theyve gotten extremely crap at 4u.

 

[mojako]

just find the typical volume of each (any) slice.
Take the slice perpendicular to the axis of rotation.

If the thickness (or thinnes since it's meant to be thin) is dx, express everything in the volume expression in terms of x. do this by using the eqn of the curve you're given.
once you have everything in terms of x, sum the typical volumes by integration.
btw I have a summary in http://www.boredofstudies.org/community/showthread.php?t=37555
there are many examples in the volumes and mechanics section.
in the others, they are more theoritical... at the moment at least.

 

[jessum]

ahaa u know what the stupidest thing is
i can do volumes by slicing. i have no problem with it. what i cant do is cylindrical shells
i cant even get the name right. grrrrrr
someone shoot me before i stuff up anymore

 

[mojako]

for cylindrical shells, do the similar thing.
take the shells parallel to the axis of rotation..
find the circumference and height. that's basically it.
circumference is 2 pi times radius.
c'mon, be more positive towards yourself ^^

 

[:: ck ::]

think of this shortcut

delta V = 2 * pi * r * h * delta r

if u are forgetful

 

[jessum]

thanks!! thats a very clear way to look at it
it makes sense now
its like slicing sorta but ur adding up volumes rather than areas?? probably not..
but something maybe vaguely like that
ill try and bluff my way through the exam

 

[mojako]

>> its like slicing sorta but ur adding up volumes rather than areas?? <<
It's a bit likely although in slicing you're also adding volumes.

To ryan (jessum can simply ignore it):
Are we allowed to use that shortcut method?
I mean, do we have to find the volume of the shell by substracting the volume of the larger cylinder by the smaller cylinder?
coz Cambridge book actually shows that in every 1 of its worked exercise.

 

[kimmeh]

we're not allowed to simply quote that 2(pi)xy thing. you have to derive it yourself each time

 

[mojako]

But can you just draw a cylindrical shell and say that its width will be.. say, delta x, and its height is xxx.. and its circumference is xxxxx
and therefore its volume is circumference * height * width, if you cut the shell and unroll it
??

(so you don't need to derive it using by takin the difference in volumes of two cylinders, one having a radius delta x less than the other)

 

[cj_bridle]

ive been told to always quote that its the inner circumference x ht x thickness .. so then you should be able to just draw it and assume that when u unravell it out it will work..

 

[cj_bridle]

oh also.. does anyone know whether in volumes: do you always have to put in the sigma notation step as the sum of the volumes/slices is from bla to bla then state what it is... or can you jump straight to the integral?

 

[CrashOveride]

@ cj: I've also wondered that. Technically you should, but I know in my case my teacher never cared. In summary, yes.

 

[mojako]

>> ive been told to always quote that its the inner circumference <<
It doesn't matter whether it's the inner or outer, because the thickness is infitely small so the inner circumference practically equals the outer one.
And I think you can show that by deriving the shell formula as a difference of the volumes of two cylinders.
whether you let the radius of the larger cylinder be R and the smaller be R-dx,
or the smaller be R and the larger be R+dx,
you will get the same result.

So from your posts I think we can quote that formula ^^ ... with a bit of word/sentence explanation of what we're doing

about the sigma:
I'm quite sure that you need to put
lim(dx-->0) sigma blablabla..., then
integral of blablabla...

But you don't have to write two lines containing sigma notation (one is the approximation without "lim" and the other has the "lim")

 

[cj_bridle]

okay thanx mojako.. have to break my habbit now..

 

[mojako]

I actually just looked at some solutions to trials papers (my teacher gives us a series really thick bundles of papers... he's crazy!!)...
my findings:

1. all of them assume typical volume of cylindrical shell as circumference x height x thickness, and you just have to draw a kind of thin block to show the unrolled shell without writin sophisticated lengthy words of explanation

2. some papers write the lim thing and some don't... from the papers I got, most trials from schools write the lim, while most papers from institutions (NEAP, Heffernan, S & G, and the like) do not. RC (or whatever it is, I dont have a clue.. it's got an horizontally flipped R and a C in its logo) writes the lim. It (RC) shows the first mark given next to the lim expression, but that may well be for finding the delta V expression. A trial from Western Region shows inconsistency (one question shows the lim and another doesn't)
Some schools (only 1 that I've seen) give a mark for finding the typical volume expression and another mark just for writing the volume of all slices/shells as a limitting sum. But sadly this school writes "Volume of all slices is: delta V = lim (deta x -> 0) sigma... delta x" haha.... and it's not just in one (solution to) question so the teacher must have seriously misunderstood it.

I suppose you could write the limiting sum of "delta A delta x" instead of "the expression for delta V". It's my personal opinion. Why don't ask mr buchanan... Are you reading sir?

boredofstudies.org... hurry up!! load yourself on my browser window!
is it faster on certain people's computers?

 

[mojako]

I actually just looked at some solutions to trials papers (my teacher gives us a series really thick bundles of papers... he's crazy!!)...
my findings:

1. all of them assume typical volume of cylindrical shell as circumference x height x thickness, and you just have to draw a kind of thin block to show the unrolled shell without writin sophisticated lengthy words of explanation

2. some papers write the lim thing and some don't... from the papers I got, trials from schools write the lim, while from institutions (NEAP, Heffernan, S & G, and the like) do not.
And apparently one school writes "delta V = lim (deta x -> 0) sigma... delta x" haha.... and it's not just in one (solution to) question so the teacher must have seriously misunderstood it.

 

[cj_bridle]

thats a good find mojako ... might wait for a more authoritive opinion...

btw: it changes speed for me.. sometimes its normal.. sometimes its slow, sometimes it doesnt load at all

 

[mojako]

yea it changes speed on my PC too

 

[kimmeh]

In the HSC theyre not concernd about that limit sigma thing. But your school may have an emphasis on it. Our school tells us we have to include it otherwise we dont get the full marks
in terms of cylindrical shells i got taught: ( (outer radisu)^2 - (inner radius)^2 )(pi) x height of shell

 

[mojako]

In the HSC theyre not concernd about that limit sigma thing. But your school may have an emphasis on it. Our school tells us we have to include it otherwise we dont get the full marks
in terms of cylindrical shells i got taught: ( (outer radisu)^2 - (inner radius)^2 )(pi) x height of shell

that's for slicing ^^

You should be able to use that for cylindrical shells too but it wil be even harder than using circumference * height * thickness