Would your expressions for the integrands be valid above z=2?Tapias5000 said:
ummm I don't understand what you mean by this, could you give me another example?haruspex said:
I saw that there were several formulas depending on the case, but I doubt that my professor would like me to use them.haruspex said:
The denominator in your fifth equation gives the volume as ##\int_0^2\pi y^2dz##. That is based on an element thickness dz at height z having volume ##\pi y^2dz##.Tapias5000 said:
Yes, it can be hard knowing which standard results you are allowed to quote. But students would be expected to know the formula for the simplest case, and that is all you need here. The method to get from the simplest case to this more general one is certainly worth knowing. Do you see how to do it?Tapias5000 said:
Hmm, the problem tells us to locate the centroid of the area shaded in blue in Z, and according to the figure that is a known data from 0 to 2, right?haruspex said:
There are several formulas, so I would not know which one to apply here.haruspex said:
Yes, but you asked what the bounds should be on the integrations, (0,2) or (0,4).Tapias5000 said:
Of which the simplest is that for a conical form extending from a plane base to a point the distance of the mass centre from the base is 1/4 the distance of the point from the base.Tapias5000 said:
aaa already understand.haruspex said:
you mean the formula ## h / 4 ##?haruspex said:
Yes. The concept is finding the mass centre of an object by representing it as the sum or difference of simpler objects.Tapias5000 said:
no, I really couldn't understand it, can you show me a different example?haruspex said:
Should I look up the definition of the center of mass for a cone?Tapias5000 said:
The definition of the centre of mass does not depend on the shape. Do you mean the formula for the center of mass for a cone? It's one quarter of the way from the base to the tip.Tapias5000 said:
damn I suck at this lmaoharuspex said:
For the two cubes problem, take moments about a point in the middle of the base of the lower cube. The result should be the same treating it as one object or two.Tapias5000 said:
To find the centroid of a cone in Z, you will need to use the formula:
x = (1/4)h
y = (1/4)h
z = (1/3)h
Where h is the height of the cone.
The centroid of a cone in Z is an important point as it represents the center of mass of the cone. This point can be used to calculate the moment of inertia and other important physical properties of the cone.
No, you cannot use any point to find the centroid of a cone in Z. The formula mentioned above only works for cones that have their base on the xy-plane and their axis along the z-axis. For other types of cones, you will need to use different formulas.
You can verify if you have correctly located the centroid of a cone in Z by checking if the coordinates you have calculated satisfy the equation of the centroid mentioned in the first question. You can also use the coordinates to calculate the moment of inertia and compare it to the known value for a cone to check for accuracy.
Yes, there are alternative methods for finding the centroid of a cone in Z. One method is by using integration to find the volume and then calculating the moment of the cone with respect to each axis. Another method is by dividing the cone into smaller, simpler shapes and finding the centroid of each shape, then using the weighted average method to find the overall centroid of the cone.