The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle θ = 35o by a brace that is attached to a pin. The beam has a weight of 342 N. Three additional forces keep the beam in equilibrium. The brace applies a force P¯ to the right end of the beam that is directed upward at the angle θ with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component H¯ and a vertical component V¯. Find the magnitudes of these three forces.

College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle θ = 35o by a brace that is attached to a pin. The beam has a weight of 342 N. Three additional forces keep the beam in equilibrium. The brace applies a force P¯ to the right end of the beam that is directed upward at the angle θ with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component H¯ and a vertical component V¯. Find the magnitudes of these three forces.

The diagram illustrates a simple structural system consisting of a vertical element labeled as "Hinge," a horizontal element labeled as "Beam," and a diagonal element labeled as "Brace." The Beam is connected to the Hinge and extends horizontally, terminating at a point labeled "Pin." The Brace forms a triangle by connecting the Pin and the Hinge and is inclined at an angle labeled \( \theta \).

The main elements are:
- **Hinge**: Acts as a support that allows rotation.
- **Beam**: A horizontal structural member.
- **Brace**: A diagonal support providing stability to the structure.
- **Pin**: A point where the Beam and Brace meet.
- **Angle \( \theta \)**: The angle between the Beam and the Brace.

This setup demonstrates basic concepts in structural engineering, showing how different components interact to maintain stability.
Transcribed Image Text:The diagram illustrates a simple structural system consisting of a vertical element labeled as "Hinge," a horizontal element labeled as "Beam," and a diagonal element labeled as "Brace." The Beam is connected to the Hinge and extends horizontally, terminating at a point labeled "Pin." The Brace forms a triangle by connecting the Pin and the Hinge and is inclined at an angle labeled \( \theta \). The main elements are: - **Hinge**: Acts as a support that allows rotation. - **Beam**: A horizontal structural member. - **Brace**: A diagonal support providing stability to the structure. - **Pin**: A point where the Beam and Brace meet. - **Angle \( \theta \)**: The angle between the Beam and the Brace. This setup demonstrates basic concepts in structural engineering, showing how different components interact to maintain stability.
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