• Jul 29th 2010, 02:33 AM
noteiler
basin has a form of cylinder with height of 0,5 meters and background radius of 0,3 meters. calculate a work that is needed to evacuate the water from the basin.

my solution: area of background = $Pi \cdot R^2$
as water has density of 1000 and $F=m \cdot g$ then
$A=m \cdot g \cdot x=882 \cdot Pi \cdot x$ and integrating the last expression from 0 to 0,5 i get 346,36 but an answer given for this problem is 346,54.

basin has a form of half of a sphere with radius 0,1 meters. calculate a work needed to evacuate water from it.

my solution: are of circle that is x meters under the center is
$Pi \cdot r^2 = Pi(R^2 - x^2) = Pi(0,01 - x^2)$
$A=m \cdot g \cdot h =Pi(0,01 - x^2) \cdot 10^4 \cdot x$
and as i integrate it from 0 to 0,1 i get 0,79, but the answer given is 1,54.
• Jul 29th 2010, 03:04 AM
Vlasev
For the first one, I did the example myself and used g = 9.8 and got your value. Using a value of g = 9.805, I got 346.537, which rounded gives the desired result. However, I looked it up and got a value of 9.806 from Gravity of Earth - Wikipedia, the free encyclopedia (third paragraph).

If you take 9.789 at the equator, you get 345.97
And if you take 9.832 at the poles, you get 347.492

So I guess you should expect a small variation in your answer, depending on the exact constants used.

For the second part, it is somewhat ambiguous. Which way is the hemisphere facing?
• Jul 29th 2010, 03:58 AM
noteiler
ok, thanks for the first one. it is good if this variation in answer is caused by constants. the main thing i wanted to check whether i have applied the integral correctly.
for the second i thought the same way, but only difference would be that area of background is function of x.
• Jul 29th 2010, 04:26 AM
Vlasev
No problem. I think you have applied the integral correctly. For the second case, judging by your picture, I think you've done the integration correctly. I did the calculation too and again used 9.805. I got 0.770083, which is 1/2 of 1.540166, which rounded to 3 sig figs is 1.54. It's possible that the answer in the book is off by a factor of 2 itself!
• Jul 29th 2010, 04:46 AM
noteiler
thanks alot. hope that it is a wrong answer in the book:D