9. The members of a truss are pin connected at joint O. Determine the magnitudes of F,and F2 for equilibrium. Set 0 = 60°.

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**ENGR 2301**

**9.** The members of a truss are pin connected at joint O. Determine the magnitudes of \( F_1 \) and \( F_2 \) for equilibrium. Set \( \Theta = 60^\circ \).

*Diagram Explanation:*
The diagram for question 9 shows a joint O with multiple forces acting on it. There are four forces labeled around the joint: a vertical force of 5 kN pointing upwards, a horizontal force of 7 kN pointing to the left, \( F_1 \) acting at a downward angle from the horizontal, and \( F_2 \) acting at an upward angle. The angle between the horizontal and \( F_1 \) is labeled as 30°.

**10.** Determine the magnitude and direction \( \Theta \) of F so that the particle is in equilibrium.

*Diagram Explanation:*
The diagram for question 10 shows a particle with three forces acting on it. There is an 8 kN force acting horizontally to the right, a 4 kN force acting vertically downward, and a third force (labeled as 5 kN) acting at an angle, which needs to be determined for equilibrium.

**Answers:**

1-4: DCCD  
5: \( 54 \, \text{N} \)  
6: \( 60 \, \text{N} \)  
7: \( R = 409 \, \text{N}, F = 504 \, \text{N}, P = 1099 \, \text{N} \)  
8: \( F_{AB} = 478 \, \text{lb}, F_{AC} = 518 \, \text{lb} \)  
9: \( F_1 = 1.83 \, \text{kN}, F_2 = 9.60 \, \text{kN} \)  
10: \( F = 3.96 \, \text{kN}, \Theta = 82.2^\circ \)  

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This text describes exercises involving equilibrium of forces in a truss and a particle, along with diagrams for visual reference. The answers section provides calculated solutions for the given problems.
Transcribed Image Text:**ENGR 2301** **9.** The members of a truss are pin connected at joint O. Determine the magnitudes of \( F_1 \) and \( F_2 \) for equilibrium. Set \( \Theta = 60^\circ \). *Diagram Explanation:* The diagram for question 9 shows a joint O with multiple forces acting on it. There are four forces labeled around the joint: a vertical force of 5 kN pointing upwards, a horizontal force of 7 kN pointing to the left, \( F_1 \) acting at a downward angle from the horizontal, and \( F_2 \) acting at an upward angle. The angle between the horizontal and \( F_1 \) is labeled as 30°. **10.** Determine the magnitude and direction \( \Theta \) of F so that the particle is in equilibrium. *Diagram Explanation:* The diagram for question 10 shows a particle with three forces acting on it. There is an 8 kN force acting horizontally to the right, a 4 kN force acting vertically downward, and a third force (labeled as 5 kN) acting at an angle, which needs to be determined for equilibrium. **Answers:** 1-4: DCCD 5: \( 54 \, \text{N} \) 6: \( 60 \, \text{N} \) 7: \( R = 409 \, \text{N}, F = 504 \, \text{N}, P = 1099 \, \text{N} \) 8: \( F_{AB} = 478 \, \text{lb}, F_{AC} = 518 \, \text{lb} \) 9: \( F_1 = 1.83 \, \text{kN}, F_2 = 9.60 \, \text{kN} \) 10: \( F = 3.96 \, \text{kN}, \Theta = 82.2^\circ \) --- This text describes exercises involving equilibrium of forces in a truss and a particle, along with diagrams for visual reference. The answers section provides calculated solutions for the given problems.
**ENGR 2301**

4. Which of the following is correct about the free body diagram of a car resting on level ground?
A) There will be only one force in the free body diagram.
B) There will be three forces in the free body diagram.
C) There will be no force in the free body diagram.
D) There will be two forces in the free body diagram.

**Free-Response Questions**

5. The system is in equilibrium as shown. If the undeformed length of the spring is 2 m, what is the weight of the hanging block?

   *Description of Diagram:*
   - A horizontal beam is attached to a vertical wall.
   - A spring with a stiffness of \( k = 30 \, \text{N/m} \) extends horizontally from the wall to the end of the beam.
   - The beam has a length of 2 m.
   - A block is hanging vertically from the end of the beam.

6. The two cables shown carry a 100 N vertical load. Most nearly, what is the tension in cable AB?

   *Description of Diagram:*
   - Two cables, labeled AB and AC, form an inverted V shape.
   - The cables are attached to point A and create equal angles with the vertical line that supports the 100 N load.

7. Determine the magnitudes of the forces P, R, and F required for equilibrium of point O.

   *Description of Diagram:*
   - Three forces, labeled P, R, and F, act at point O.
   - Forces P and R form angles of 30° and 45° with the horizontal line, respectively.
   - A 600 N force acts vertically downward at point O.

8. The crate has a weight of 550 lb. Determine the force in each supporting cable.

   *Description of Diagram:*
   - A crate labeled D is suspended by two cables.
   - Cable AB forms a 30° angle with the vertical and is connected to point B.
   - Cable AC forms a 45° angle with the vertical and is connected to point C.
   - Both cables converge at point A above the crate.
Transcribed Image Text:**ENGR 2301** 4. Which of the following is correct about the free body diagram of a car resting on level ground? A) There will be only one force in the free body diagram. B) There will be three forces in the free body diagram. C) There will be no force in the free body diagram. D) There will be two forces in the free body diagram. **Free-Response Questions** 5. The system is in equilibrium as shown. If the undeformed length of the spring is 2 m, what is the weight of the hanging block? *Description of Diagram:* - A horizontal beam is attached to a vertical wall. - A spring with a stiffness of \( k = 30 \, \text{N/m} \) extends horizontally from the wall to the end of the beam. - The beam has a length of 2 m. - A block is hanging vertically from the end of the beam. 6. The two cables shown carry a 100 N vertical load. Most nearly, what is the tension in cable AB? *Description of Diagram:* - Two cables, labeled AB and AC, form an inverted V shape. - The cables are attached to point A and create equal angles with the vertical line that supports the 100 N load. 7. Determine the magnitudes of the forces P, R, and F required for equilibrium of point O. *Description of Diagram:* - Three forces, labeled P, R, and F, act at point O. - Forces P and R form angles of 30° and 45° with the horizontal line, respectively. - A 600 N force acts vertically downward at point O. 8. The crate has a weight of 550 lb. Determine the force in each supporting cable. *Description of Diagram:* - A crate labeled D is suspended by two cables. - Cable AB forms a 30° angle with the vertical and is connected to point B. - Cable AC forms a 45° angle with the vertical and is connected to point C. - Both cables converge at point A above the crate.
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