A horizontally positioned door weighing 1200 N is held in place by hinges centered at points A and B and a taut rope stretched between points D and E. The hinges facilitate "smooth" rotation about the x-axis, and point C coincides with the door's center of gravity. Questions: (a) Sketch a free-body diagram of the door, showing all possible forces and reactions exerted on the door. (b) Is the problem statically determinate or indeterminate in its current form? Jus- tify your answer. (c) If the hinge at point B is broken and physically disconnected from the door, such that the door is now only supported at points A and D, is the problem statically determinate or indeterminate? Justify your answer. (d) Assuming the scenario in part (c), solve for the reaction forces and moments at hinge A and the tension T in the cable.

A horizontally positioned door weighing 1200 N is held in place by hinges centered at points A and B and a taut rope stretched between points D and E. The hinges facilitate "smooth" rotation about the x-axis, and point C coincides with the door's center of gravity. Questions: (a) Sketch a free-body diagram of the door, showing all possible forces and reactions exerted on the door. (b) Is the problem statically determinate or indeterminate in its current form? Jus- tify your answer. (c) If the hinge at point B is broken and physically disconnected from the door, such that the door is now only supported at points A and D, is the problem statically determinate or indeterminate? Justify your answer. (d) Assuming the scenario in part (c), solve for the reaction forces and moments at hinge A and the tension T in the cable.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Educational Exercise on Statics

A horizontally positioned door weighing 1200 N is held in place by hinges centered at points A and B and a taut rope stretched between points D and E. The hinges facilitate “smooth” rotation about the x-axis, and point C coincides with the door’s center of gravity.

**Questions:**

(a) Sketch a free-body diagram of the door, showing all possible forces and reactions exerted on the door.

(b) Is the problem statically determinate or indeterminate in its current form? Justify your answer.

(c) If the hinge at point B is broken and physically disconnected from the door, such that the door is now only supported at points A and D, is the problem statically determinate or indeterminate? Justify your answer.

(d) Assuming the scenario in part (c), solve for the reaction forces and moments at hinge A and the tension T in the cable.

**Diagram Explanation:**

The diagram illustrates a door supported by hinges at points A and B. A cable runs from point D on the door to a fixed point E. Key dimensions and coordinates include:

- Dimensions of the door: 2.0 m by 1.5 m.
- The position of point C (center of gravity): (-0.75, 1, 0).
- The position of point D: (0.25, 2, 0).
- The position of point E above D: 3 m vertically and 0.5 m horizontally offset.
- The location of point A: (0, 0, 0).

The diagram shows the orientation within a 3D coordinate system (x, y, z) and provides visual reference for measuring distances and applying forces.

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