### Mechanics of the Human Arm – Educational Exercise**Description:**The arm depicted in the figure below weighs **37.6 N**. The force of gravity acting on the arm operates through point **A**. Your task is to determine the magnitudes of both the tension force **\(\vec{F_t}\)** within the deltoid muscle and the force **\(\vec{F_s}\)** exerted by the shoulder on the humerus (upper-arm bone) to maintain the arm in the shown position. Please provide your answers to the nearest newton.**Formulas & Calculation:**- **Force of Gravity (\(\vec{F_g}\))**: 37.6 N- **Distance from point A (\(\vec{F_g}\))**: 0.290 m- **Angle θ (the angle between \(\vec{F_s}\) and \(\vec{F_t}\))**: 12°- **Distance from point O (\(\vec{F_t}\))**: 0.080 m**Diagram Analysis:**The diagram below provides a visual representation. The arm is held horizontal with point O representing the shoulder joint and point A indicating where the gravity force acts. The forces in the system are:1. **\(\vec{F_t}\)**: The tension force exerted by the deltoid muscle, which acts upward and to the left at an angle \(θ = 12°\) from the horizontal axis.2. **\(\vec{F_s}\)**: The shoulder force exerted on the humerus, which acts vertically upwards.3. **\(\vec{F_g}\)**: The gravitational force acting downwards through point A.**Procedure for Calculation:**1. **Sum of the torques around point O**: Taking the counterclockwise direction as positive.2. **Sum of the forces in the vertical direction**: Considering equilibrium conditions, since the arm is stationary.3. **Sum of the forces in the horizontal direction**: Ensuring that all forces in the system balance out.**Inputs for Calculation:**- \( \vert F_t \vert \cos(12^\circ) \)- \( \vert F_s \vert \)- \( \vert F_g \vert \)**Provide Answers:**- **\( F_t \)**: \( \_\_\_\_\_\_\_ \text{

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The arm in the figure below weighs 37.6 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force F, in the deltoid muscle and the force i, exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. (Enter your answers to at least the nearest newton.) F, = N 12° 0.080 m 0.290 m

The arm in the figure below weighs 37.6 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force F, in the deltoid muscle and the force i, exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. (Enter your answers to at least the nearest newton.) F, = N 12° 0.080 m 0.290 m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

### Mechanics of the Human Arm – Educational Exercise

**Description:**
The arm depicted in the figure below weighs **37.6 N**. The force of gravity acting on the arm operates through point **A**. Your task is to determine the magnitudes of both the tension force **\(\vec{F_t}\)** within the deltoid muscle and the force **\(\vec{F_s}\)** exerted by the shoulder on the humerus (upper-arm bone) to maintain the arm in the shown position. Please provide your answers to the nearest newton.

**Formulas & Calculation:**
- **Force of Gravity (\(\vec{F_g}\))**: 37.6 N
- **Distance from point A (\(\vec{F_g}\))**: 0.290 m
- **Angle θ (the angle between \(\vec{F_s}\) and \(\vec{F_t}\))**: 12°
- **Distance from point O (\(\vec{F_t}\))**: 0.080 m

**Diagram Analysis:**
The diagram below provides a visual representation. The arm is held horizontal with point O representing the shoulder joint and point A indicating where the gravity force acts. The forces in the system are:

1. **\(\vec{F_t}\)**: The tension force exerted by the deltoid muscle, which acts upward and to the left at an angle \(θ = 12°\) from the horizontal axis.
2. **\(\vec{F_s}\)**: The shoulder force exerted on the humerus, which acts vertically upwards.
3. **\(\vec{F_g}\)**: The gravitational force acting downwards through point A.

**Procedure for Calculation:**
1. **Sum of the torques around point O**: Taking the counterclockwise direction as positive.
2. **Sum of the forces in the vertical direction**: Considering equilibrium conditions, since the arm is stationary.
3. **Sum of the forces in the horizontal direction**: Ensuring that all forces in the system balance out.

**Inputs for Calculation:**
- \( \vert F_t \vert \cos(12^\circ) \)
- \( \vert F_s \vert \)
- \( \vert F_g \vert \)

**Provide Answers:**
- **\( F_t \)**: \( \_\_\_\_\_\_\_ \text{

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