**Educational Exercise: Static Mechanics****Diagram Description:**The diagram shows a hatch modeled as a rigid body in a three-dimensional Cartesian coordinate system. The hatch is supported and held in place by a hinge at point A, a roller at point B, and a rope connecting point C to D. The dimensions and angles are given to determine the forces acting on the hatch.- **Coordinate System:** The hatch lies in the xy-plane. The z-axis is vertical.- **Point A:** Located at the bottom left corner on the xy-plane, with the hatch pivoted around it. It serves as a hinge.- **Point B:** Located 2 meters along the y-axis and slightly elevated at a 30° angle from the xy-plane.- **Point C:** Located at the bottom edge center of the hatch, positioned 1.4 meters along the x-axis.- **Point D:** Elevated 1 meter above the xy-plane along the z-axis and located 1.2 meters from point B.- **Rope CD:** Connects point C on the hatch to point D, creating tension.**Task Instructions:**A) **Draw a Free Body Diagram** Draw a free body diagram of the hatch (75 kg) to assess all forces acting on it. Make necessary assumptions for static determinacy.B) **Compute Rope Tension** Calculate the tension in the rope connecting point C to D.C) **Compute Reactions at A and B** Determine the reaction forces at the hinge (A) and the roller (B) needed to maintain equilibrium.The problem involves using principles of statics to determine the forces and reactions in a system subjected to constraints and external forces.

Given: The mass of the hatch, m = 75 kg

1.2 m 1.4 m Im D B 2 m 30° A) Draw a Free Body Diagram of the 75 kg hatch. Make an assumption to keep the problem statically determinate. B) Compute the tension in the rope. C) Compute the reactions at A and B.

1.2 m 1.4 m Im D B 2 m 30° A) Draw a Free Body Diagram of the 75 kg hatch. Make an assumption to keep the problem statically determinate. B) Compute the tension in the rope. C) Compute the reactions at A and B.

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: Static Mechanics**

**Diagram Description:**

The diagram shows a hatch modeled as a rigid body in a three-dimensional Cartesian coordinate system. The hatch is supported and held in place by a hinge at point A, a roller at point B, and a rope connecting point C to D. The dimensions and angles are given to determine the forces acting on the hatch.

- **Coordinate System:** The hatch lies in the xy-plane. The z-axis is vertical.
- **Point A:** Located at the bottom left corner on the xy-plane, with the hatch pivoted around it. It serves as a hinge.
- **Point B:** Located 2 meters along the y-axis and slightly elevated at a 30° angle from the xy-plane.
- **Point C:** Located at the bottom edge center of the hatch, positioned 1.4 meters along the x-axis.
- **Point D:** Elevated 1 meter above the xy-plane along the z-axis and located 1.2 meters from point B.
- **Rope CD:** Connects point C on the hatch to point D, creating tension.

**Task Instructions:**

A) **Draw a Free Body Diagram**
Draw a free body diagram of the hatch (75 kg) to assess all forces acting on it. Make necessary assumptions for static determinacy.

B) **Compute Rope Tension**
Calculate the tension in the rope connecting point C to D.

C) **Compute Reactions at A and B**
Determine the reaction forces at the hinge (A) and the roller (B) needed to maintain equilibrium.

The problem involves using principles of statics to determine the forces and reactions in a system subjected to constraints and external forces.

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