Where Is the Center of Mass of a Leg?

[epuen23]

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?


ANSWER:

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?

ANSWER:
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

 

[Chestermiller]

Please define the parameters in your equations.

 

[epuen23]

I hope this helps.

 

[epuen23]

Please define the parameters in your equations.

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

 

[scottdave]

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

 

[scottdave]

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?

 

[epuen23]

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]

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.

 

[epuen23]

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