Skip to main content

Huge letter billboard


The application of mathematics in life is not only to calculate the addition, subtraction, multiplication, and division of various numbers. It also includes applications to many things in life. For example, when we are building a new building, we have to calculate many things, such as Weighing of the building, calculating the position of the weighing column, and the method of delivering materials to the roof. The concept of center of mass is involved here. The center of mass is the center of the mass of an item. If this center can be found, it will be easier to hoist the item, and at the same time, some dangers (decoupling due to uneven weight) will be avoided. It is very simple to simply transport some steel bars, because the center of mass can be found directly. But for example, for some strange shapes, such as the name of a company, those huge letters, such objects need to be calculated to find its center of mass.

Then we take the letter F as an example, because its center of mass cannot be seen directly, and it is not too complicated, which also helps us to explore.

The length of each side of it is shown in the figure
We also divide him into three, three rectangles, we find their centroids respectively, if the lower left corner is regarded as the origin (0.0), then the three rectangles are called a, b and c respectively.
a is composed of points A, B, J, K. b is composed of points C, D, E, F. c is composed of points G, H, I, J.

Then, I can find the centroids of the three rectangles at a(0.2,1.25),b(0.8,1.3),c(0.9,2.3). So here we need to start some calculations, here is the equation for calculating the centroid:
Because it is a uniform quality, then use the area to express the quality.

The coordinates of the mass point x: (0.4*2.5)*0.2+(0.4*0.8)*0.8+(0.4*1)*0.9=((0.4*2.5)+(0.4*0.8)+(0.4*1))*x.

The coordinates of the mass point y: (0.4*2.5)*1.25+(0.4*0.8)*1.3+(0.4*1)*2.3=((0.4*2.5)+(0.4*0.8)+(0.4*1))*y

Finally, we can find that the coordinates of the center of mass is (0.474,1.503)
It looks like it is on the image, but in fact its center of mass is not on the "F", it is on the outside.
By the way, I gave it a thickness of 0.2, so its true center of mass is (0.474, 1.503, 0.1)
Labels:

Comments

Post a Comment

Popular posts from this blog

Knot 9-31

Knot 9-31 A knot is mathematics is defined as a closed, non-self-intersecting curve that is placed in three dimensions and cannot be the "unknot". The main difference between a knot in the real world and a known in mathematics is that a knot in mathematics does not contain any extra strands. The example following will help visualize this. Today, I have specifically chosen knot 9-31 from the Knot Atlas. This knot is very unique and contains some very interesting properties that we are going to look into. The Crossing Number For my knot today, I chose knot 9-31 from the Knot Atlas. This knot contains 9 crossings! The Unknotting Number The unknotting number is exactly what is sounds like. This is the minimum number of times the knot must be passed through itself to untie it. Luckily, the Knot Atlas is super useful and provides the unknotting number for us, but I still...
Post a Comment
Read more

Do Over: Integration for Over Regions in the Plane

Introduction Earlier in the semester, we visited the topic of integration for over region regions in the plane. This was our first experience with taking integration in the third dimension. To do this, we had to use double integrals to calculate the volume of a region between two surfaces. This topic seems relatively straightforward and anyone who has taken a higher calculus class knows of double integrals. Today, we are going to revisit this topic for a couple of reasons. Why Double Integrals Again? As mentioned before, I am revisiting this topic for a couple of reasons. One of the main reasons is due to how the 3D print turned out. Due to the function, I chose, the final rectangular prism was stand alone. When printing, this resulted in a sloppy prism that lacked structural integrity. The image below is a reference to my original design that includes the prism that had the issue. The main cause of ...
Post a Comment
Read more

Middle of Mass Measured from Moment

The center of mass of an object is the point that lies in the average position of mass in that object. For a normal polygon, that point is in the middle of the shape. However, if the shape is irregular, has concave angles, or has holes, the center of mass can be far from the middle of the object. Two things come into factor when determining the center of mass of an object. Weight and distance. Obviously, if one side of an object has more mass than the other, the center of mass will be on the heavier side. But, distance plays a role, too. If two sides of an object have the same mass, but one is farther from the middle, the center of mass will be on the side that has farther mass. Multiplying both of these factors together gives the moment of an object. Dividing the moment by the overall mass gives the location of the center of mass.   The reason I chose my shape is to mimic how those toy balancing birds work. The toy is a model bird with its wings outstretched. The ...
Post a Comment
Read more