Question

Many aspects of a gymnast's motion can be modeled by representing the gymnast by four segments consisting of arms, torso (including the head), thighs, and lower legs, as in the figure below.

Figures a and b describe a gymnast's motion as he swings about a bar.

1. A side-view of the gymnast as he swings about the bar. The gymnast's back is horizontal, his arms are vertical, his thighs are at an angle of 60° to the horizontal, and his lower legs are approximately horizontal.
2. A simplified diagram of the gymnast is superimposed on an xy plane with the origin defined as the intersection of the gymnast's arm and torso. The arm is along the y-axis, the torso is along the x-axis, the thigh is at an angle of 60° above the x-axis, and the leg is horizontal. At the approximate centers of each of the above-mentioned body parts are circled X shapes. Each circled X has an arrow pointing to it, where each of these arrows originates from the nearest joint and points, up, right, or up and to the right.

In the figure, (b) shows arrows of lengths r_cg locating the center of gravity of each segment. Use the data below and the coordinate system shown in figure (b) to locate the center of gravity of the gymnast shown in figure (a). Masses for the arms, thighs, and legs include both appendages. (Enter your answers in m, to at least three significant figures.)

Answer 1

y components of the centre of gravity of lenym mest. 3 Yegory = (com - (Yeg)m] = 0.548 – 0-236 = 0.312 m асат – оч Ś you gothi = (Veg. tu sinbos) = (0-145 519600) = 0.1255 m - 7 Yeg, leg = (tai Sin60) = 10.372 x sinbo) = 0.32216 m Yeg = {Marm Yegram + Motor Yog tar f Mth Yeg the Amig ? Marm + Motor IMA I May 1X0-3/2) +(33.6% )+(14-1 % 0-1255 72 +(7-58*0.325 V wygley 6.81 $.3326 +14414 758 Yeg = 0.10191 = 10.101 M De 0 1