Static Equilibrium Cable Problem

In summary, a 50.0 kg square sign is hung from a 3.00 m horizontal rod attached to a wall with a cable. The tension in the cable and the horizontal and vertical components of the force from the wall on the rod are being calculated. The equations of net force and net torque are used to solve the problem. The vertical component from the wall on the rod is explained through the concept of the sign's resultant weight acting through its center of gravity.
  • #1
Seraph404
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Homework Statement



PhysProb20Ch13.jpg


In fig. 13-32, a 50.0 kg uniform square sign, 2.00 m on a side, is hung from a 3.00 m horizantal rod of negligible mass. A cable is attached to the end of the rod and to a point on the wall 4.00 m above the point where the rod is hinged to the wall. (a) What is the tension in the cable? What are the magnitudes and directions of the (b) horizantal and (c) vertical components of the force on the rod from the wall?


Homework Equations



Net force = zero
Net torque = zero


The Attempt at a Solution



I don't understand how there is a vertical component exerted by the wall onto the rod.
 
Last edited:
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  • #2
If the weight of the sign was all concentrated at the right corner, there would be no vert comp of the wall on the rod; however, the sign's resultant weight acts thru its c.g., not at the corner. Try summing torques about the top left corner.
 
  • #3
All right. Thanks so much!
 

What is a static equilibrium cable problem?

A static equilibrium cable problem is a type of physics problem that involves analyzing the forces acting on a cable or rope that is suspended between two points in a state of equilibrium. This means that the cable is not moving and the forces acting on it are balanced.

How do you solve a static equilibrium cable problem?

To solve a static equilibrium cable problem, you must first draw a free-body diagram of the cable, which shows all the forces acting on it. Then, you can use the equations of equilibrium to determine the unknown forces and angles. These equations include the sum of all forces in the x-direction, the sum of all forces in the y-direction, and the sum of all moments.

What are the assumptions made in a static equilibrium cable problem?

There are three main assumptions made in a static equilibrium cable problem: first, the cable is assumed to be massless, meaning that its weight can be ignored. Second, the cable is assumed to be inextensible, meaning that it does not stretch or compress under the applied forces. Finally, the cable is assumed to be perfectly flexible, meaning that it can bend easily without breaking.

What types of structures or systems can be analyzed using static equilibrium cable problems?

Static equilibrium cable problems can be used to analyze a variety of structures and systems, including suspension bridges, cranes, and even human body movements. They are also commonly used in engineering and architecture to determine the forces acting on cables in a structure.

What are some real-world applications of static equilibrium cable problems?

Static equilibrium cable problems have many practical applications, such as determining the tension in a rope used to lift heavy objects, analyzing the forces acting on a zip line or ski lift, and designing cable-supported structures like suspension bridges or cable-stayed buildings. They are also used in biomechanics to study the forces exerted on joints and muscles during human movements.

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