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Free-Response Questions 7. Resolve F2 in the figure into its x and y components. 300 N F- 450 N F- 600 N 45 ENGR 2301 8. Two forces act on the hook. Determine the magnitude of the resultant force. 30 200 N 40 500 N

Free-Response Questions 7. Resolve F2 in the figure into its x and y components. 300 N F- 450 N F- 600 N 45 ENGR 2301 8. Two forces act on the hook. Determine the magnitude of the resultant force. 30 200 N 40 500 N

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Can someone please show all the work for these problems please?
**Free-Response Questions** **7. Resolve \( F_2 \) in the figure into its x and y components.** Diagram Description: - There is a triangle with an angled tension force \( F_2 = 600 \, \text{N} \). - The angle from the horizontal x-axis is \( 45^\circ \). - Another force \( F_1 = 450 \, \text{N} \) acts vertically upwards. --- **ENGR 2301** **8. Two forces act on the hook. Determine the magnitude of the resultant force.** Diagram Description: - A hook is shown with two forces: - \( 500 \, \text{N} \) force at a \( 40^\circ \) angle below the horizontal. - \( 200 \, \text{N} \) force at a \( 30^\circ \) angle above the horizontal. **9. Determine the magnitude and direction of the resultant force.** Diagram Description: - A hook with three forces acting on it: - \( 200 \, \text{N} \) vertically upwards. - \( 300 \, \text{N} \) horizontally to the right. - \( 400 \, \text{N} \) at an angle to the right, below the horizontal. **10. Determine the design angle for connecting member A to the plate if the resultant force is to be directed vertically upward. Also, what is the magnitude of the resultant?** Diagram Description: - A diagram of a plate with two forces: - \( F_A = 500 \, \text{N} \). - \( F_B = 400 \, \text{N} \) aligned horizontally. **11. The cable AO exerts a force on the top of the pole of \( F = \{-120i - 90j - 80k\} \). If the cable has a length of 34 ft, determine the height \( z \) of the pole and the location \((x,y)\) of its base.** Diagram Description: - A pole with cable and coordinate axes \( X, Y, Z \) is shown to explain the forces acting on it. This section involves breaking down forces into components, calculating resultants, and solving for unknowns in static systems.
Transcribed Image Text:**Free-Response Questions** **7. Resolve \( F_2 \) in the figure into its x and y components.** Diagram Description: - There is a triangle with an angled tension force \( F_2 = 600 \, \text{N} \). - The angle from the horizontal x-axis is \( 45^\circ \). - Another force \( F_1 = 450 \, \text{N} \) acts vertically upwards. --- **ENGR 2301** **8. Two forces act on the hook. Determine the magnitude of the resultant force.** Diagram Description: - A hook is shown with two forces: - \( 500 \, \text{N} \) force at a \( 40^\circ \) angle below the horizontal. - \( 200 \, \text{N} \) force at a \( 30^\circ \) angle above the horizontal. **9. Determine the magnitude and direction of the resultant force.** Diagram Description: - A hook with three forces acting on it: - \( 200 \, \text{N} \) vertically upwards. - \( 300 \, \text{N} \) horizontally to the right. - \( 400 \, \text{N} \) at an angle to the right, below the horizontal. **10. Determine the design angle for connecting member A to the plate if the resultant force is to be directed vertically upward. Also, what is the magnitude of the resultant?** Diagram Description: - A diagram of a plate with two forces: - \( F_A = 500 \, \text{N} \). - \( F_B = 400 \, \text{N} \) aligned horizontally. **11. The cable AO exerts a force on the top of the pole of \( F = \{-120i - 90j - 80k\} \). If the cable has a length of 34 ft, determine the height \( z \) of the pole and the location \((x,y)\) of its base.** Diagram Description: - A pole with cable and coordinate axes \( X, Y, Z \) is shown to explain the forces acting on it. This section involves breaking down forces into components, calculating resultants, and solving for unknowns in static systems.
**Problem 11:** The cable AO exerts a force on the top of the pole with a force vector of \( \mathbf{F} = \{-120i - 90j - 80k\} \). Given that the cable has a length of 34 ft, determine the height \( z \) of the pole and the coordinates \((x, y)\) of its base. *Diagram Description:* This diagram shows an illustration of a pole with a force \(\mathbf{F}\) acting at the top. The coordinate axes \((x, y, z)\) are shown to indicate the directions. --- **ENGR 2301** **Problem 12:** The force has a component of 20 N directed along the negative y-axis. Represent the force \(\mathbf{F}\) as a Cartesian vector. *Diagram Description:* The diagram depicts a force vector making an angle of 150° with the y-axis, with a labeled component of 20 N along the negative y-axis. --- **Problem 13:** Determine the component of projection of the force \(\mathbf{F}\) along the pipe AB. *Diagram Description:* This diagram illustrates a force \(\mathbf{F} = \{-20i - 30j + 60k\} \, \text{lbs}\) applied, with points A, B, and pipe orientation given in three-dimensional space. The setup includes spatial dimensions of 2 ft, 4 ft, and 3 ft along different axes. --- **Answers:** 1-6: ABBCAB, B 7: \( F_{2x} = -318.2 \, \text{N}, \, F_{2y} = 318.2 \, \text{N} \) 8: 666 N 9: \( F_R = 567 \, \text{N}, \, \theta = 38.1^\circ \)
Transcribed Image Text:**Problem 11:** The cable AO exerts a force on the top of the pole with a force vector of \( \mathbf{F} = \{-120i - 90j - 80k\} \). Given that the cable has a length of 34 ft, determine the height \( z \) of the pole and the coordinates \((x, y)\) of its base. *Diagram Description:* This diagram shows an illustration of a pole with a force \(\mathbf{F}\) acting at the top. The coordinate axes \((x, y, z)\) are shown to indicate the directions. --- **ENGR 2301** **Problem 12:** The force has a component of 20 N directed along the negative y-axis. Represent the force \(\mathbf{F}\) as a Cartesian vector. *Diagram Description:* The diagram depicts a force vector making an angle of 150° with the y-axis, with a labeled component of 20 N along the negative y-axis. --- **Problem 13:** Determine the component of projection of the force \(\mathbf{F}\) along the pipe AB. *Diagram Description:* This diagram illustrates a force \(\mathbf{F} = \{-20i - 30j + 60k\} \, \text{lbs}\) applied, with points A, B, and pipe orientation given in three-dimensional space. The setup includes spatial dimensions of 2 ft, 4 ft, and 3 ft along different axes. --- **Answers:** 1-6: ABBCAB, B 7: \( F_{2x} = -318.2 \, \text{N}, \, F_{2y} = 318.2 \, \text{N} \) 8: 666 N 9: \( F_R = 567 \, \text{N}, \, \theta = 38.1^\circ \)
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