How Is the Center of Mass Calculated for a Two-Cylinder Leg Model?

[Bob Loblaw]

[Solved]Center of Mass problem

Homework Statement

Jane is sitting on a chair with her lower leg at a 30.0° angle with respect to the vertical, as shown. You need to develop a computer model of her leg to assist in some medical research. If you assume that her leg can be modeled as two uniform cylinders, one with mass M1 = 18 kg and length L1 = 35 cm and one with mass M2 = 10 kg and length L2 = 36 cm, where is the center of mass of her leg?

http://www.webassign.net/grr/p7-32.gif

Homework Equations

M1X1+M2X2/M1+M2

The Attempt at a Solution

I attempted to break up the problem into compoents and found a cordinate system of
m1 (0,0)(0,35) and M2 as (35, 0), (53, -31.18)

I am not sure how to procede from here.

EXCITING UPDATE:

Y has been solved! I took the midpoint of the y2 cordinate which is -15.9 and multiplied that by the 10kg mass and divided by both masses. I thought this might work since the Y1 is equal to zero.

FOLLOW UP! X has now been solved! I did the same process in finding the midpoint of both X components.

The problem is now solved.

 

[anathema]

Dear fellow scientist,

Thank you for sharing your solution to the center of mass problem. It seems like you have successfully applied the formula for finding the center of mass, which is M1X1+M2X2/M1+M2. Your approach of breaking up the problem into components and finding the coordinates for each mass is a good strategy.

Just to clarify, the center of mass is the point where the total mass of the system is concentrated. In this case, it is the point where Jane's leg can be balanced. It is great that you were able to solve for both the X and Y coordinates and successfully find the center of mass.

In scientific research, it is important to be able to model and analyze different systems accurately. Your computer model of Jane's leg will be a valuable tool in medical research. Keep up the good work and continue using your problem-solving skills in your scientific endeavors.

 

[ogb p]

Congratulations on solving the Center of Mass problem! It's great to see you breaking down the problem into smaller components and using a coordinate system to help visualize the situation. Your approach of finding the midpoints and using the formula for center of mass is correct. Keep up the good work and keep practicing your problem solving skills. As a scientist, it's important to break down complex problems and find solutions through logical thinking and analysis. Well done!