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lena2383
Radio Wave
USA
13 Posts |
 Posted - 02/17/2003 : 04:16:15
Here is a problem that I am having trouble with can you help
here is the diagram http://shinyobjects.netfirms.com/cross.htmlthanks lena
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alexander
Gamma Wave
Russia
3982 Posts |
Posted - 02/17/2003 : 13:36:17
4.1 cm3, 0.82 cm2, 15.3 cm2Life is chemistry,chemistry is quantum mechanics,quantum mechanics is math.To learn how natural laws,natural forces and natural objects originate from math,click: http://www.emmynoether.com/
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STAii
X-Ray Wave
Jordan
1376 Posts |
Posted - 02/17/2003 : 16:48:08
Alexander is really straight forward  .
Let me explain a little how to solve this kind of questions..
If you have an object that is made of two parallel bases, and that surface of the two bases is the same, and cross section is the same at any place (like your dove-tail), there is a rule for the volume of the object that states that the volume equals the surface of the bases times the height of the object (the vertical distance between the two bases).
So the Volume of the Dove-Tail (V) equals the area of the base (B) (which is the same as the surface of the cross section) * the height (H) (or in your drawing, the depth)
V=B*H
Since we know H (from the drawing), we only need to calculate B in order to find out V.
Now look at the cross section, and try to make its shape into smaller shapes which's area is known.
This way the area of the whole cross section will be equal to the sum of the areas of the little shapes making it.
For example i was able to make the cross section into three rectangles and two triangles (There are simpler ways ... but all will work eventually)
I got 6.3 for the cross section area
so B=6.3 cm2
Back to our equation.
V=B*H
V=6.3*5=32.5 cm3
So now we are done of the volume, and the cross section area.Let's see the surface area of the dove tail.
You can find that by making the surface area into parts (just like we did for the surface of the cross section), but you can do it in a simpler way.
The surface area of the dove-tail (call it X) equals the side-surface (call is S) + the surface of the first base + the surface of the second base
X=S+B+B
X=S+2B
We know B, we only need to know S.
If the dove tail was wrapped with a paper (so that each point on the surface of the dove tail was in contact with a point of the paper), then the surface of the paper equals S.
Try to imagine it ...
The way i see it the paper will have a rectangular shape, one of the side of this rectangle will be the Height (of Depth) (H) and the other side will be the sum-up of the sides of the cross section.
That is S = H*(3.5 + 2 + 2 + 2.2 + (3.5 - 1.9) + 2 (0.16 + ((2.2-1.9)/2)2))
(it may seem a little complicated, but it is not, it is only that i made all the calculations in a single line.
The square root comes from the fact that i used the phytagorean thereom.
Using a calculator you get
S=~H*12.1544=60.772 cm2
X=S+2B=60.772+2*6.3=60.772+12.6=73.372 cm2 This way, i completed everything (i hope so)
I hope i helped, and didn't make lot of mistakes
You've gotta be japaneese !
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Edited by - STAii on 02/17/2003 17:07:08
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