# Calculating the Center of Mass

## Homework Statement:

The center of mass of someone's thigh, shank, and foot are located at the following coordinates:

Thigh: (2.7, 3.2)

Shank: (2.1, 2.5)

Foot: (1.5, 1.9)

If the masses of them are respectively 9.6, 2.9, and 0.9 kg, where is the location of the entire leg?

CM = (2.5, 3)

## Relevant Equations:

CMx = Xprox + L%*(Xdist - Xprox)
CMy = Yprox + L%*(Ydist - Yprox)
CMbody = E*(CMseg*Mseg)/Mtotal
The center of mass of someone's thigh, shank, and foot are located at the following coordinates:
Thigh: (2.7, 3.2)
Shank: (2.1, 2.5)
Foot: (1.5, 1.9)
If the masses of them are respectively 9.6, 2.9, and 0.9 kg, where is the location of the entire leg?

CM = (2.5, 3)

I'm having trouble figuring out the steps for this. I feel like I need to know the Length % in order to complete the formula but am lost as to how to get this. Thank you for any help you may be.

-E

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Chestermiller
Mentor

I hope this helps.

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I was having a hard time uploading screenshots of the equations/problem. I think I got it to work now.

scottdave
Homework Helper
So in the bottom of the screenshot, it talks about calculating the torques for each segment. Do you know how to do that?

scottdave
Homework Helper
Think about a simpler problem, like a 1 dimensional bar with weights attached at different points. How would you find the center of mass? Now how would this be expanded to 2 dimensions?

Think about a simpler problem, like a 1 dimensional bar with weights attached at different points. How would you find the center of mass? Now how would this be expanded to 2 dimensions?
So I know T (Torque) = F (Force) * ⊥d (Perpendicular Distance).
Would it be: 2.7 * 9.6? Am I even close?

Chestermiller
Mentor
So I know T (Torque) = F (Force) * ⊥d (Perpendicular Distance).
Would it be: 2.7 * 9.6? Am I even close?
Yes, you're on the right track.

Yes, you're on the right track.
Oh my gosh, thank you so much guys!!!!

X
2.7 * 9.6 = 25.92
2.1 * 2.9 = 6.09
1.5 * 0.9 = 1.35
SUM OF TORQUES = 33.39
DIVIDED BY SUM OF MASS = 13.4
33.39 / 13.4 = 2.5

Y
3.2 * 9.6 = 30.72
2.5 * 2.9 = 7.25
1.9 * 0.9 = 1.71
SUM OF TORQUES = 39.68
DIVIDED BY SUM OF MASS = 13.4
39.68 / 13.4 = 3

• scottdave and Chestermiller