### Understanding Forces in Equilibrium**Problem Statement:**The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle \( \theta = 36^\circ \) by a brace that is attached to a pin. The beam has a weight of 334 N. Three additional forces keep the beam in equilibrium. The brace applies a force \( \vec{P} \) to the right end of the beam that is directed upward at the angle \( \theta \) 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.**Solution:**(a) \( V = \)(b) \( P = \)(c) \( H = \)**Diagram:**- The diagram illustrates a horizontal beam supported at the left end by a hinge and at the right end by a brace.- Hinge is shown at the left end of the beam providing support.- The beam is horizontally positioned.- A brace is attached at an angle \( \theta = 36^\circ \).- The force applied by the brace \( \vec{P} \) is directed upward at an angle \( \theta \).- The horizontal component \( H \) and vertical component \( V \) are the forces applied by the hinge.**Analysis:**To solve for \( V \), \( P \), and \( H \), follow the principles of static equilibrium which state that the sum of all forces and the sum of all moments about any point must be zero.**Note:**Ensure to decompose forces into their respective components and apply the equilibrium conditions.

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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 0 = 36° by a brace that is attached toa pin. The beam has a weight of 334 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 0 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. Beam Hinge Pin Brace (a) V = (b) P = i (c) H =i

The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle 0 = 36° by a brace that is attached toa pin. The beam has a weight of 334 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 0 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. Beam Hinge Pin Brace (a) V = (b) P = i (c) H =i

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Problem 1.1MA

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Pressure Vessels

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### Understanding Forces in Equilibrium

**Problem Statement:**
The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle \( \theta = 36^\circ \) by a brace that is attached to a pin. The beam has a weight of 334 N. Three additional forces keep the beam in equilibrium. The brace applies a force \( \vec{P} \) to the right end of the beam that is directed upward at the angle \( \theta \) 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.

**Solution:**

(a) \( V = \)

(b) \( P = \)

(c) \( H = \)

**Diagram:**
- The diagram illustrates a horizontal beam supported at the left end by a hinge and at the right end by a brace.
- Hinge is shown at the left end of the beam providing support.
- The beam is horizontally positioned.
- A brace is attached at an angle \( \theta = 36^\circ \).
- The force applied by the brace \( \vec{P} \) is directed upward at an angle \( \theta \).
- The horizontal component \( H \) and vertical component \( V \) are the forces applied by the hinge.

**Analysis:**
To solve for \( V \), \( P \), and \( H \), follow the principles of static equilibrium which state that the sum of all forces and the sum of all moments about any point must be zero.

**Note:**
Ensure to decompose forces into their respective components and apply the equilibrium conditions.

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