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. 60° Thigh Ex Arm 60° Torso Leg x In the figure, (b) shows arrows of lengths rcg 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.)

Elements Of Electromagnetics
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### Modeling a Gymnast's Motion

Many aspects of a gymnast's motion can be effectively modeled by representing the gymnast using four segments: the arms, torso (including the head), thighs, and lower legs. This is illustrated in the figures below.

#### Figure Descriptions:

- **Figure (a):** Illustrates a gymnast in a specified pose with legs raised, forming an angle of 60° from the horizontal.
  
- **Figure (b):** Displays a segmented model of the gymnast. Each segment (arm, leg, thigh, torso) is shown with arrows indicating the center of gravity (\( r_{cg} \)) of each segment within the coordinate system.

#### Table of Segment Data:

| Segment | Mass (kg) | Length (m) | \( r_{cg} \) (m) |
|---------|-----------|------------|------------------|
| Arms    | 6.81      | 0.548      | 0.242            |
| Torso   | 33.6      | 0.613      | 0.337            |
| Thighs  | 14.1      | 0.378      | 0.149            |
| Legs    | 7.50      | 0.350      | 0.227            |

#### Instructions:

- Use the data provided and the coordinate system shown in figure (b) to determine the center of gravity of the entire gymnast as shown in figure (a).
- The mass values for the arms, thighs, and legs include both appendages.
- Ensure that all answers are recorded in meters, with at least three significant figures. 

This model aids in understanding how the distribution and alignment of body segments affect balance and movement during gymnastics.
Transcribed Image Text:### Modeling a Gymnast's Motion Many aspects of a gymnast's motion can be effectively modeled by representing the gymnast using four segments: the arms, torso (including the head), thighs, and lower legs. This is illustrated in the figures below. #### Figure Descriptions: - **Figure (a):** Illustrates a gymnast in a specified pose with legs raised, forming an angle of 60° from the horizontal. - **Figure (b):** Displays a segmented model of the gymnast. Each segment (arm, leg, thigh, torso) is shown with arrows indicating the center of gravity (\( r_{cg} \)) of each segment within the coordinate system. #### Table of Segment Data: | Segment | Mass (kg) | Length (m) | \( r_{cg} \) (m) | |---------|-----------|------------|------------------| | Arms | 6.81 | 0.548 | 0.242 | | Torso | 33.6 | 0.613 | 0.337 | | Thighs | 14.1 | 0.378 | 0.149 | | Legs | 7.50 | 0.350 | 0.227 | #### Instructions: - Use the data provided and the coordinate system shown in figure (b) to determine the center of gravity of the entire gymnast as shown in figure (a). - The mass values for the arms, thighs, and legs include both appendages. - Ensure that all answers are recorded in meters, with at least three significant figures. This model aids in understanding how the distribution and alignment of body segments affect balance and movement during gymnastics.
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