How to judge the change of the center of gravity and three ways to determine the center of gravity

If you can't use the hanging method, then use the parallel knife method.

Two parallel knives slowly joined together. The object is placed on it, and then when it merges, the vertical plane where the blade is located passes through the center of gravity, and it is done in three different directions, and then the three planes determine one point, and that point is the center of gravity.

Because of the back-bending of the human body, the center of gravity is not in the human body, but behind the human body.

So the center of gravity passes under the crossbar.

It's like a circle of iron, thrown upwards, if it happens to touch the roof at the highest time, the center of gravity of the hoop must be lower than the height of the roof.

The mass of the object will be divided equally by the plane of the center of gravity, which is determined by the nature of the mass.

There are two very important concepts here, one is called the center of mass and the other is called the particle.

An object can be seen as an infinite number of particles, and the center of gravity coincides with the center of mass.

And the definition of the centroid is to make a vector from this centroid to all the particles, and the sum of these vectors is 0

So if the object is divided into two parts through the plane of the centroid, the sum of the two conjunctive vectors composed of the particles in the two parts is 0

Therefore, these two composite vectors must be equal in size and opposite in opposite directions, because there is a relationship of equal size, so the mass of the object is equally divided.

Who told you that"The mass of the object will be divided equally by the plane of the center of gravity", kid?!

The center of gravity is the geometric mean point of mass.

The three ways to determine the center of gravity are as follows:

1. Geometric method.

For objects with uniform mass distribution and certain geometric shapes, its center of gravity is at a certain point in the object, such as rods and thin plates, which coincide with its geometric center, while some objects with uniform mass distribution and regular shape have their center of gravity coincident with its geometric center, but not necessarily on the object, such as a metal circle with uniform texture.

Generally speaking, the center of gravity of an object with a symmetry plane is on its symmetry plane, the center of gravity of an object with a symmetry line is on its symmetry line, and the center of gravity of an object with a symmetry point falls on the symmetry point.

2. Suspension method.

Hang the irregular sheet at a certain point A, when the sheet is stationary, accompany Ming to draw a vertical AB on the sheet along the hanging line, and then choose another point C to hang it again, and draw a vertical line CD on the sheet again.

3. Traction method.

Hang one end of the long rod-shaped sail object with a string AB, and slowly pull the other end with an elastic string CD to the corresponding position, draw the extension lines of AB and CD respectively, and intersect at point E, and point O directly above point E is the center of gravity of the rod. The principle of finding the center of gravity of the traction method is: when the object is in equilibrium by three forces, the lines of action of the three forces must intersect at one point.

The center of gravity is the point at which the resultant force of all the constituent fulcrums of the gravity force passes through the object in any direction in the gravitational field. It's called the center of gravity

The center of gravity of a regular and uniform object is its geometric center. The center of gravity of an irregular object can be determined by the suspension method. The center of gravity of an object, not necessarily on the object.

The position of the center of gravity of the object, the mass is evenly distributed.

The position of the center of gravity is only related to the shape of the object. For example, the center of gravity of a uniform thin straight rod is at the midpoint of the rod, the center of a uniform sphere is at the center of the sphere, and the center of gravity of a uniform cylinder is at the midpoint of the axis. The center of gravity of an irregular object can be determined by the suspension method.

The center of gravity of an object, not necessarily on the object.

In the case of an object with uneven mass distribution, the position of the center of gravity is not only related to the shape of the object, but also to the distribution of mass within the object. Trucks.

The center of gravity changes with how much is loaded and the loading position, and the center of gravity of the crane changes with the weight and height of the object being lifted.

If a line or slice of the center of gravity divides an object or figure into two parts, the volume or area of the two parts is not necessarily equal. (Not all lines or slices that are over the center of gravity bisect the area or volume of an object or shape, such as the center of gravity of a regular triangle.)

And a straight line on the parallel side divides the triangle into two parts with an area ratio of 4:5. About this, the principle of leverage in physics can be used.

Explanation: The distance from the center of gravity of the two pieces divided into two figures to the center of gravity of the triangle is equivalent to the two arms of the lever.

And the area of the two figures is equivalent to the two forces of the lever. Because the center of gravity is equivalent to the area of two figures"Centralized"(refer to the definition of center of gravity). As in the above example, the distance from the center of gravity of the two graphs to the center of gravity of the triangle is exactly equal to 5:

4。If you are interested, you can use a ruler to draw a drawing.

Prove. )Mathematically determining the position of the center of gravity of an object:

Take any definite spatial Cartesian coordinate system in the space where an object (total mass m) is located.

o-xyz, then the object can be derived from i particles, each of which corresponds to its own coordinates (xi, yi, zi) and mass mi, knowing m=m1+m2+ +mi, let the center of gravity of the object be g(x,y,z).

then x=(x1m1+x2m2+ +ximi) m

y=(y1m1+y2m2+‥+yimi)/m

z=(z1m1+z2m2+‥+zimi)/m

The center of gravity is the point at which the resultant force of the Earth on each tiny part of the gravitational pull of an object. Every tiny part of an object is subject to gravity (see Gravitational Force), which can be approximated as a system of intersecting forces at the center of the Earth.

Since the size of an object is much smaller than the radius of the Earth, the gravitational force acting on an object in general can be approximated as a parallel force system, and the total weight of the object is the resultant force of these gravitational forces.

Refers to the intersection of the three midlines of a triangle. The center of gravity refers to the point at which the Earth's resultant force applies to each small part of the gravitational force in an object. Considered the point of concentration of the total weight of the object.

The point at which the resultant force of gravity on the parts of the object is applied, without changing the shape of the object. The ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint of the opposite edge is 2:1.

In physics, the center of gravity refers to the point at which the Earth's resultant force applies to every tiny part of the gravitational pull of an object.

The center of gravity in mathematics refers to the intersection of the three middle lines of the triangle, and its proof theorem is the dovetail theorem or Seva's theorem, and the application theorem is Menelaus's theorem and Seva's theorem.

Center of gravity: 1In physics, it refers to the point of action of the resultant force of gravity on an object, which is called the center of gravity.

2.Metaphorically as the center or important part of a thing.

The center of gravity refers to the point at which the resultant force of gravity is applied to the parts of an object. It also refers to the core or main part of a thing.

Hello, happy to answer your questions. Focus: The center or main part of the matter. Synonyms are, center, emphasis. Focus. Sentence formation: I put all my focus on English.

The center of gravity is the point at which the resultant force of the Earth on each tiny part of the gravitational pull of an object.

1.Mechanically, it refers to the point of action of the resultant force of gravity on each part of the object.

2.The center or main part of the matter.

3.Geometrically, it refers to the midpoint where the three midlines of a triangle intersect.

In junior high school physics, the center of gravity is like this.

The point at which gravity works on an object is called the center of gravity.

The lower the center of gravity, the more stable the object is. Objects are not easy to turn over.

Mathematically Center of gravity: the intersection of the three middle lines, the three middle lines of the triangle intersect at one point The center of gravity: the intersection of the three middle lines, the three middle lines of the triangle intersect at one point, and the distance from this point to the vertex is twice the distance from it to the midpoint of the opposite side; Vertical Heart:

the intersection of three high triangles; Heart: The intersection of the bisector of the three inner angles, is three.

The point at which the resultant force of gravity is applied to the parts of an object.

The center of gravity is the point at which the resultant force of gravity is applied to all parts of the body. It can also represent the intersection of the three middle lines of a triangle. It can also be said to be the center of the work, the main part of the matter.

Categories: Education Science >> Admission >> College Entrance Examination Problem Description:

For example, measure an iron piece, and then fold the iron piece to find that the center of gravity has changed, and then for example"Limb Bush dorsal jump"Why does their center of gravity change like this? And not some other location?

Analysis: When jumping back, the details of the athlete's pole crossing should be carefully analyzed. First the head and shoulders over the pole, at this time the head and shoulders are in the highest position on the whole body, then the back and hips are in turn over the pole, at this time the back and hips are in the highest part of the whole body, the head and shoulders have descended to the bottom of the pole after crossing the pole, the foot is the last to cross the pole, the foot is the highest part of the body when the foot passes the pole, and the rest of the parts have passed the pole and are all below the pole.

In short, the parts of the body are gradually crossed in turn, and the cherry blossom part of the body is always the highest part of the body when it is the turn to cross the pole, and it seems that the body is always "hanging" on the pole softly (only the point of "hanging" on the body is changing).

The center of gravity macro does hail.

All parts of an object are subject to gravity. In terms of effect, we can think that the gravitational force on each part is concentrated in one point, which is called the center of gravity of the object.

For objects with uniform mass distribution (homogeneous objects), the position of the center of gravity is only related to the shape of the object. For an object with a regular shape, its center of gravity is on the geometric center of gravity, for example, the center of a uniform thin straight bar is at the midpoint of the rod, the center of gravity of a uniform object is at the center of the sphere, and the center of gravity of a uniform cylinder is at the midpoint of the axis. The center of gravity of an irregular object can be determined by the suspension method.

The center of gravity of an object, not necessarily on the object.

For objects with uneven mass distribution, the position of the center of gravity is not only related to the shape of the object, but also related to the distribution of mass in the object. The center of gravity of a truck changes with how much is loaded and where it is loaded, and the center of gravity of a crane changes with the weight and height of the object being lifted.

Several properties of the center of gravity:

1. The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1.

2. The area of the three triangles composed of the center of gravity and the three vertices of the triangle is equal.

3. The sum of squares of the distance from the center of gravity to the three vertices of the triangle is the smallest.

4. In the planar Cartesian coordinate system, the coordinates of the center of gravity are the arithmetic mean of the vertex coordinates, that is, the coordinates of the center of gravity are (1 3, 1 3, 1 3).

The ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint of the opposite edge is 2:1.

The area of the three triangles formed by the center of gravity and the three vertices of the triangle is equal. The sum of the squares of the 3 vertices from the center of gravity to the triangle is minimum. The center of gravity is the point where the product of the distance from the triangle to the three sides is the largest.

The nature and proof of the center of gravity.

1. The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1.

Proof: It is known that abc, e, f are the midpoints of ab, ac. EC and FB are handed over to G.

Verification: eg=1 2cg.

The nature and proof of the center of gravity.

Proof: Pass E as EH BF to AC to H.

ae=be，eh//bf。

ah=hf=1 2af (proportionality theorem for parallel line segments).

and af=cf.

hf=1/2cf。

hf:cf=1/2。

eh∥bf。

eg:cg=hf:cf=1/2。

eg=1/2cg。

A few theorems:

Center of gravity theorem: The three middle lines of a triangle intersect at a point where the point is to the vertex.

The distance is 2 times the distance from it to the midpoint of the opposite side. This point is called the center of gravity of the triangle.

Centroid theorem: The perpendicular bisector of the three sides of a triangle intersects at a point. Destroy the outer center of the point called the triangle.

Perpendicular theorem: three high crossings with or triangles are at one point in the rest of the story. This point is called the vertical center of the triangle.

Inner theorem: The bisector of the three inside angles of a triangle intersects at one point. This point is called the triangle of the heart.

Centroid theorem: The bisector of one inner angle of a triangle and the bisector of the outer angle at the other two vertices intersect at one point. This point is called the paracentrium of the triangle. The triangle has three paracentricities.