A 6.8kg cat is standing on a uniform beam that weighs 245.0 N. The beam is supported by a hinge along the wall and a cable attached at the end of the 8.00m long beam at an angle of 33° to the horizontal, as shown. A 4.5kg uniform sign that is 2.00m in width hangs from the end of the beam, so that the right edge of the sign is aligned with the end of the beam. The beam is in equilibrium. If the cat is standing 1.5m away from the wall, find:

International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter10: Virtual Work And Potential Energy
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**Title: Physics Problem: Equilibrium and Forces on a Beam**

**Problem Description:**

A 6.8 kg cat is standing on a uniform beam that weighs 245.0 N. The beam is supported by a hinge along the wall and a cable attached at the end of the 8.00 m long beam at an angle of 33° to the horizontal, as shown. A 4.5 kg uniform sign that is 2.00 m in width hangs from the end of the beam, so that the right edge of the sign is aligned with the end of the beam. The beam is in equilibrium. If the cat is standing 1.5 m away from the wall, find:

a. The tension in the cable

b. The horizontal component of support force supplied by the hinge

c. The vertical component of the support force supplied by the hinge

**Diagram Explanation:**

The diagram shows a right triangle with a beam extending horizontally from a wall. A cable is attached to the beam and leads upwards at a 33° angle from the horizontal. A cat icon is placed on the beam, representing the cat 1.5 m from the wall. A rectangle labeled "sign" hangs vertically at the edge of the beam.

**Key Points:**

- The beam length is 8.00 m.
- The cat is 1.5 m from the wall.
- The sign is 2.00 m wide.
- The cable and beam create a 33° angle with the horizontal.
- The system is in equilibrium, meaning net forces and torque are zero.

This problem requires applying principles of static equilibrium to solve for forces acting on the system, such as using the torque and force balance equations.
Transcribed Image Text:**Title: Physics Problem: Equilibrium and Forces on a Beam** **Problem Description:** A 6.8 kg cat is standing on a uniform beam that weighs 245.0 N. The beam is supported by a hinge along the wall and a cable attached at the end of the 8.00 m long beam at an angle of 33° to the horizontal, as shown. A 4.5 kg uniform sign that is 2.00 m in width hangs from the end of the beam, so that the right edge of the sign is aligned with the end of the beam. The beam is in equilibrium. If the cat is standing 1.5 m away from the wall, find: a. The tension in the cable b. The horizontal component of support force supplied by the hinge c. The vertical component of the support force supplied by the hinge **Diagram Explanation:** The diagram shows a right triangle with a beam extending horizontally from a wall. A cable is attached to the beam and leads upwards at a 33° angle from the horizontal. A cat icon is placed on the beam, representing the cat 1.5 m from the wall. A rectangle labeled "sign" hangs vertically at the edge of the beam. **Key Points:** - The beam length is 8.00 m. - The cat is 1.5 m from the wall. - The sign is 2.00 m wide. - The cable and beam create a 33° angle with the horizontal. - The system is in equilibrium, meaning net forces and torque are zero. This problem requires applying principles of static equilibrium to solve for forces acting on the system, such as using the torque and force balance equations.
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