Verify that the force in the elbow joint in the figure below is 407 N, as stated in the text. (Submit a file with a maximum size of 1 MB.)

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Chapter1: Units, Trigonometry. And Vectors
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The image depicts a biomechanical analysis of forces acting on a human arm while holding a weight. The diagram includes a simplified drawing of an arm with a free-body diagram.

### Description:

- **Arm Diagram**: 
  - The arm is shown holding a box labeled "PHYSICS" with a mass \( m_b = 4.0 \, \text{kg} \).
  - The arm itself is marked with a mass \( m_s = 2.5 \, \text{kg} \).
  - The biceps muscle exerts a force \( F_B \) upwards.
  - The triceps muscle is also indicated, although it does not directly exert a force shown in the diagram.
  - The weight of the arm (\( w_a \)) acts downward at a distance of 16 cm from the elbow.
  - The weight of the box (\( w_b \)) acts downward at a distance of 38 cm from the elbow.
  - The force at the elbow joint (\( F_E \)) acts upward.

- **Free-Body Diagram**:
  - Displays forces at play:
    - \( F_B \) is represented upwards.
    - \( w_a \) (weight of the arm) and \( w_b \) (weight of the box) are shown acting downwards.
    - \( F_E \), the force at the elbow joint, acts upwards.

### Measurements:
- **Distances** from the elbow:
  - Center of mass of the arm (CG) is 16 cm.
  - The box is held 38 cm from the elbow.

### Purpose:
The exercise is to verify that the force in the elbow joint is 407 N, as stated. This involves calculating the torques and forces involved in holding the weight steady.

### Application:
This type of analysis is crucial for understanding the mechanics of human movement and the stresses on joints during physical activities. It aids in designing ergonomic tools and preventing injuries.
Transcribed Image Text:The image depicts a biomechanical analysis of forces acting on a human arm while holding a weight. The diagram includes a simplified drawing of an arm with a free-body diagram. ### Description: - **Arm Diagram**: - The arm is shown holding a box labeled "PHYSICS" with a mass \( m_b = 4.0 \, \text{kg} \). - The arm itself is marked with a mass \( m_s = 2.5 \, \text{kg} \). - The biceps muscle exerts a force \( F_B \) upwards. - The triceps muscle is also indicated, although it does not directly exert a force shown in the diagram. - The weight of the arm (\( w_a \)) acts downward at a distance of 16 cm from the elbow. - The weight of the box (\( w_b \)) acts downward at a distance of 38 cm from the elbow. - The force at the elbow joint (\( F_E \)) acts upward. - **Free-Body Diagram**: - Displays forces at play: - \( F_B \) is represented upwards. - \( w_a \) (weight of the arm) and \( w_b \) (weight of the box) are shown acting downwards. - \( F_E \), the force at the elbow joint, acts upwards. ### Measurements: - **Distances** from the elbow: - Center of mass of the arm (CG) is 16 cm. - The box is held 38 cm from the elbow. ### Purpose: The exercise is to verify that the force in the elbow joint is 407 N, as stated. This involves calculating the torques and forces involved in holding the weight steady. ### Application: This type of analysis is crucial for understanding the mechanics of human movement and the stresses on joints during physical activities. It aids in designing ergonomic tools and preventing injuries.
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