# Center of mass of the human figure

• shaka23h
In summary, the problem involves finding the center of mass of a human figure in a sitting position. The figure is divided into three parts with their respective masses and coordinates given. Using the equation Xcm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3), the x coordinate of the center of mass is calculated to be 0.27437 m. The same equation is used to find the y coordinate, which is 0.307 m. The mass of the head is not included in the calculation since its x coordinate is the same as the torso, neck, and head's y coordinate. The final coordinates are both positive values, as the head's y coordinate
shaka23h
The drawing shows a human figure approximately in a sitting position. For the purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass = 41.5 kg) with a center of mass located on the y-axis at a point 0.359 m above the origin, (2) the upper legs (mass = 15.2 kg) with a center of mass located on the x-axis at a point 0.153 m to the right of the origin, and (3) the lower legs and feet (total mass = 9.06 kg) with a center of mass located 0.478 to the right of and 0.299 m below the origin. Find the (a) x coordinate and (b) the y coordinate of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the whole-body mass) has been ignored to simplify the drawing.

I can't submit the drawing, but I'm really stumped on this problem. Perhaps some kind of hint to get me started? I know how to find the center of mass of something but the X and Y coordinates? Help!

shaka23h said:
The drawing shows a human figure approximately in a sitting position. For the purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass = 41.5 kg) with a center of mass located on the y-axis at a point 0.359 m above the origin, (2) the upper legs (mass = 15.2 kg) with a center of mass located on the x-axis at a point 0.153 m to the right of the origin, and (3) the lower legs and feet (total mass = 9.06 kg) with a center of mass located 0.478 to the right of and 0.299 m below the origin. Find the (a) x coordinate and (b) the y coordinate of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the whole-body mass) has been ignored to simplify the drawing.

I can't submit the drawing, but I'm really stumped on this problem. Perhaps some kind of hint to get me started? I know how to find the center of mass of something but the X and Y coordinates? Help!
Don't you apply the "seesaw principle"? Fulcrumology?

A 1 pound weight, 2 feet from the fulcrum will be balanced by a 2 pound weight 1 foot from the fulcrum.

I've never heard of that before. The only equation that I could use is Xcm = m1x1 + m2x2.../ m1 + m2... how would I apply it though :(

Thanks

shaka23h said:
The only equation that I could use is Xcm = m1x1 + m2x2.../ m1 + m2...
That's exactly the equation you need. You have the coordinates and mass of each piece. Use that equation to find the x and y coordinates of the center of mass of the entire body. (You'll need to apply it twice, once for x-coordinates, once for y-coordinates.)

Xcm = (m1x1 + m2x2 + ...)/(m1 + m2 + ...)

ok this is what I have so far.

Xcm = (15.2)(.153)+ (9.06)(.478)/ (15.2 + 9.06) From this I got .27437. I've submitted this answer for online grading and its not it... I get a total of 5 tries.

Ycm = (15.2)(.153)+ (9.06)(.478) / (15.2+ 9.06)

Doc you have any clue what I'm doing wrong?

Thanks

You left out one of the pieces! You forgot the "torso, neck, and head". (The "+ ..." in the center of mass equation indicates that you keep on adding terms for all the pieces... m1, m2, m3, m4, whatever. In this problem, you have three pieces to consider so you must extend the equation appropriately.)

First thing for you to do: Write out the center of mass equation for three pieces.

http://img230.imageshack.us/img230/1766/ch07p44rl1.gif

here is the image of the actual problem

Last edited by a moderator:
the reason I didn't added the head is because I didn't think there is a x cordinate for it? it just says center of mass located on the y-axis at a point .39 m above the origin. Where is the x coordinate for this? Also I'm wondering if the value is below the orgin does this make it a negative value?

Thanks a lot Doc

shaka23h said:
the reason I didn't added the head is because I didn't think there is a x cordinate for it? it just says center of mass located on the y-axis at a point .39 m above the origin.
Of course it has an x coordinate, just like any other point. Hint: Every point on the y-axis has the same x coordinate. What is it?
Also I'm wondering if the value is below the orgin does this make it a negative value?
Absolutely.

wow I GOT it!

you are awsome.

Thanks a lot Doc I love this forum !

## What is the center of mass of the human figure?

The center of mass of the human figure is the point where the entire mass of the body can be considered to be concentrated. It is the balance point of the body, where the weight is evenly distributed in all directions.

## Why is the center of mass important in understanding human movement?

The center of mass is important because it is the point around which the body's movements and balance are controlled. It helps us understand how the body maintains stability and changes position while performing various activities.

## How is the center of mass calculated for the human body?

The center of mass is calculated by finding the average position of all the body's individual mass points. This can be done by dividing the body into smaller segments and calculating the center of mass of each segment, then finding the overall center of mass using these individual calculations.

## Does the center of mass change for different body positions?

Yes, the center of mass changes for different body positions. It depends on the distribution of the body's mass and the position of the body segments relative to each other. For example, the center of mass will shift when a person bends or twists their body.

## How does the center of mass affect balance and stability?

The center of mass plays a crucial role in maintaining balance and stability. If the center of mass is within the base of support (the area covered by the feet), the body is stable and less likely to fall. However, if the center of mass moves outside of the base of support, the body becomes unstable and may fall. Therefore, keeping the center of mass within the base of support is essential for maintaining balance and stability.

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