Center of mass -chair and cylinders

[warrior2014]

Center of mass --chair and cylinders!

Homework Statement

Jane is sitting on a chair with her lower left at a 30° angle with respect to the vertical. 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 by 2 uniform cylinders, one with mass m1=24kg and length L1=35cm and one with mass m2=10kg and length L2=46cm, where is the center of mass of her leg?

(______ cm, _________ cm)

Homework Equations

The Attempt at a Solution

I haven't learned this as yet and have no idea how to start the problem or how to get the final answer. Any help is appreciated. Thanks!

 

[_coyote_]

The center of mass for Jane's leg can be calculated using the following equation: CM = (m1*x1 + m2*x2)/(m1+m2) Where x1 and x2 are the distances from the origin to the centers of the two cylinders. From the problem, we can determine that the angle between the left side of the chair and the vertical is 30°, so we can use trigonometry to calculate x1 and x2: x1 = L1*cos(30°) x2 = L2*cos(30°) Plugging these values into the equation for the center of mass gives us: CM = (24*(35*cos(30°)) + 10*(46*cos(30°)))/(24 + 10) Solving this equation gives us the center of mass coordinates: CM = (___ cm, ___ cm)