Mass points with four points

• soopo
In summary, the question asks to find the ratio EH:HG in a triangle ABC where D and E are trisection points of BC with D between B and E. The solution involves drawing in CG and dealing with triangle ABC, finding the location of point X where segments CG and DF intersect, and then dealing with triangle CGD. This approach avoids dealing with "four all at once." Ultimately, the point of interest can only be served by one triangle, such as CDG.

Homework Statement

Find the ratio EHG. Please, see the full question with a picture here: https://dl.getdropbox.com/u/175588/problem.JPG [Broken]

Homework Equations

"In triangle ABC, let D and E be the trisection points of BC with D between B and E." Please, see the full question with a picture here: https://dl.getdropbox.com/u/175588/problem.JPG [Broken]

The Attempt at a Solution

I am unable to calculate mass points to a line with four mass points.

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First draw in CG and deal with triangle ABC with segments CG and DF which intersect at a point, call it X. Find the location of X.

Then deal with triangle CGD.

This way you avoid dealing with "four all at once."

Billy Bob said:
First draw in CG and deal with triangle ABC with segments CG and DF which intersect at a point, call it X. Find the location of X.

Then deal with triangle CGD.

This way you avoid dealing with "four all at once."

So if we can serve one point in only one way, we are done. The point could also be served by other triangles but we must stick to the one we choose, just like you choose consider CDG.

1. What are mass points with four points?

Mass points with four points is a concept in physics where four particles or points with masses are arranged in a geometric shape, such as a triangle or parallelogram. This arrangement allows for the calculation of various properties, such as the center of mass and moment of inertia.

2. How do you calculate the center of mass for mass points with four points?

The center of mass for mass points with four points can be calculated by taking the average of the x-coordinates and the average of the y-coordinates for the four points. This point represents the center of mass for the system.

3. What is the significance of mass points with four points in physics?

Mass points with four points is a useful concept in physics for understanding the motion and properties of objects. It allows for the analysis of complex systems and the prediction of their behavior.

4. Can mass points with four points be used to calculate the moment of inertia?

Yes, mass points with four points can be used to calculate the moment of inertia for a system. The moment of inertia is a measure of an object's resistance to rotational motion and can be calculated using the masses and distances of the four points from the axis of rotation.

5. How is the concept of mass points with four points used in real-world applications?

Mass points with four points can be applied in various real-world scenarios, such as analyzing the stability of structures, predicting the motion of objects in space, and designing mechanical systems. It is also used in fields such as engineering, astronomy, and robotics.