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F, 12° F, F. 0.080 m 0.290 m- P8.7 from Serway and Vuille 9th Ed. A) Write down the two equations that come from Newton's second Law for an object in equilibrium. You should use the variables F; = |F| and F, = |F| in these equations.

F, 12° F, F. 0.080 m 0.290 m- P8.7 from Serway and Vuille 9th Ed. A) Write down the two equations that come from Newton's second Law for an object in equilibrium. You should use the variables F; = |F| and F, = |F| in these equations.

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### Diagram Description and Instructions The image is a diagram illustrating forces acting on a forearm, showing an application of Newton's second law in equilibrium. The forearm is shown with three main forces: 1. **Tension Force (\( \vec{F_t} \))**: This force is acting horizontally to the right along the forearm. 2. **Force (\( \vec{F_s} \))**: This is directed diagonally downward at an angle (\( \theta = 12^\circ \)) from the horizontal. 3. **Gravitational Force (\( \vec{F_g} \))**: This force acts vertically downward at point A, near the hand. **Distances:** - Point O is shown on the elbow, with a horizontal distance of 0.080 m from the tension force application point. - Point A is positioned where the gravitational force is applied, at a horizontal distance of 0.290 m from point O. **Task (A):** Write down the two equations that are derived from Newton’s second law for an object in equilibrium using the given variables: - \( F_t = |\vec{F_t}| \) - \( F_s = |\vec{F_s}| \) ### Explanation In equilibrium, the sum of forces and the sum of torques acting on the arm should be zero. Therefore, when analyzing the system, these two primary equations need to be established: 1. **Sum of Forces Equals Zero**: Ensures the forearm remains stationary or moves at a constant velocity. 2. **Sum of Torques Equals Zero**: Ensures the forearm does not rotate, maintaining a balance of rotational forces. Use these principles to express the equilibrium conditions in mathematical terms, incorporating all given forces and angles.
Transcribed Image Text:### Diagram Description and Instructions The image is a diagram illustrating forces acting on a forearm, showing an application of Newton's second law in equilibrium. The forearm is shown with three main forces: 1. **Tension Force (\( \vec{F_t} \))**: This force is acting horizontally to the right along the forearm. 2. **Force (\( \vec{F_s} \))**: This is directed diagonally downward at an angle (\( \theta = 12^\circ \)) from the horizontal. 3. **Gravitational Force (\( \vec{F_g} \))**: This force acts vertically downward at point A, near the hand. **Distances:** - Point O is shown on the elbow, with a horizontal distance of 0.080 m from the tension force application point. - Point A is positioned where the gravitational force is applied, at a horizontal distance of 0.290 m from point O. **Task (A):** Write down the two equations that are derived from Newton’s second law for an object in equilibrium using the given variables: - \( F_t = |\vec{F_t}| \) - \( F_s = |\vec{F_s}| \) ### Explanation In equilibrium, the sum of forces and the sum of torques acting on the arm should be zero. Therefore, when analyzing the system, these two primary equations need to be established: 1. **Sum of Forces Equals Zero**: Ensures the forearm remains stationary or moves at a constant velocity. 2. **Sum of Torques Equals Zero**: Ensures the forearm does not rotate, maintaining a balance of rotational forces. Use these principles to express the equilibrium conditions in mathematical terms, incorporating all given forces and angles.
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