How is finding the centroid useful in determining the strength of the shape?
489536
By strength I suppose you mean elastic calculation when the body is subjected to deforming forces. Actually, the centroid of a shape having an unifrom mass distirbution coincides with its center of mass. This point is central to the analysis carried out in rigid body statics and dynamics.
909019
You'll get the same strength(within reason) and the same dimensions using this method.I can't believe noone has answered this question yet.Good luck on the other site!
474415
Because of the ratio of area inside a shape compared to the outline isnt the most efficient (outline 4a cf area a^2) where a is the length of side for the square (rationalises to 4:a)\n\none would find other shapes to be more efficient like hexagons, with circles having the best ration between area and circumference (PI*d cf (PI*d^2)/2) which rationalises to 1:d/2 where d is the diameter (width) of the circle.\n\nthe circle will contain the maximum area within for the minimum circumference thus rendering it cheaper if you are say making a box for a known quantity of goods.\n\nother than that the answer can depend on what the final calculations are to be used for
881707
Determining the mass is trivial: just weigh the block.  For the density, you will need to know the volume, which will require some measuring with a ruler.  Then divide the mass by the volume for your answer.
659168
You should use density to check that out.\nDensity=Weight/Volume
841334
Easiest way would be to drop a bisector from two of the angles.  The intersection will be the centroid.  This is assuming a regular pentagon.\n\nIf it is an irregular pentagon, you could tie a weight to a string.  Hold the pentagon by a vertex while also holding the string.  This line passes through the center of gravity.  Do the same for another vertex.  The lines will intersect at the centroid (aka center of gravity).  This method would work for a regular pentagon also since the lines would be the angle bisectors.
325473
Measure the weight of 1 cup of sand and figure it from there.\n\n :-)
472886
When you put your parts together, make them in the shape of triangles. Triangles are the strongest shape for building a simple construction like the one you're making. Make your structure with many triangles. For example, if you can, make your entire structure in the shape of a triangle, and also connect the sides of the big triangle with lots of smaller ones.
796030
Depends on the supports, whether they are simple (pivot possible), or completely fixed.\n\nAlso depends on whether it is a point load, or a distributed load.\n\nThere is a technique that is taught in engineering such that you can work it out for almost any configuration, but it is a bit too involved to detail. Do a web search on 'Bending Moment Diagrams' and you will find lots on the techniques.\n\nFor specific calculation, I found a neat online calculator, go to http://www.mechengcalculations.com/index.html, and look for your beam under section 'Beam Flexure'
896595
http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/\n\nit tells you how
605315
Occular strength X Objective strength.
943665
this is impossible to answer, there are many shapes that could be made this way.  do you have any other information like right angles or angles at corners?
1127635
To solve for the centroid, treat this problem like a center of mass problem, because the centroid of an object is also the object's center of mass. To find the x coordinate of the center of mass, multiply each piece of mass by its x coordinate, add them all together, and divide the sum by the total mass. In our situation, we use y as our piece of mass, multiply it by x, and divide by the total area. Of course, we need to use integrals, and the formula looks like this:\n\nx = integral(y*x*dx) / integral(y*dx)\n\nwhere y is the difference in the two equations (2x+3-x^2).\n\nI hope you know how to do integrals, so I won't show all that work. It comes out to be (32/3) / (32/3) which is 1.\n\nThe process is similar for calculating the y coordinate, except the integrating is complicated. First, rewrite the equations into "x =" form. The total area remains the same, but you will need to break the numerator into two parts: an integral from 0 to 1 of 2 times square root y * y * dy plus an integral from 1 to 9 of (square root of y - (.5y - 1.5)) * y * dy. After evaluating, you should get (.8+532/15)/(32/3) = 3.4. The coordinates of the centroid are (1, 3.4)
608577
Depends on the shape of the object being measured.
444257
The ultimate strength of a beam is found by US = max load/CSA.  There's not a lot of math to it, but you do need to measure pretty carefully.\n\nThere comes a problem, however, where some materials "stretch" before actually failing, thus making the measurement of the max load difficult.  As an example, if you've ever pulled plastic wrap apart, it gets easier at a point right before it breaks into two.  The point where after you pull on it and it gets easier is called the yield strength.  After you pass the yield strength, you don't need as much force to cause failure in the material.\n\nNow in steel, the yield and ultimate strengths are pretty close to each other that the above discussion really doesn't affect it if you are trying to break a beam on your own.  But the ultimate strength of steel is probably something you can look up in a table somewhere.  Then you can use the above formula to see how much your beam can take based on the US and the cross sectional area.
403281
take a straw (cylinder) and ram it through a potato.  If you do it right, the straw will go right through the potato!  The cylinder is the strongest and most stable of the shapes and you can see why soups, veggies, fruits, etc. all come in cans!\n\nRight triangels, or right angles are all around you.  The floor and the wall of you room for example.  The bottom of a pool is a good example of an obtuse triangle, suspension bridges - trapezoid, if you look at the tip of a pencil - it's a cone but the shape of a cone when you look at it head on is a scalene triangle
470540
http://en.wikipedia.org/wiki/Strength_of_materials