What is the Tension in a Ladder Challenge System?

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SUMMARY

The discussion focuses on calculating the tension in a rope tied to a ladder system, specifically a ladder of length 2a and weight W, with its center of gravity located 3/8 of the way up. The ladder rests against a smooth vertical wall and a smooth horizontal plane, indicating the absence of friction. The equilibrium equations must be established to solve for the two unknown normal forces and the tension in the rope, ensuring that the sum of all forces and the net torque about the center of mass are both zero.

PREREQUISITES
  • Understanding of static equilibrium in physics
  • Knowledge of normal forces and their role in equilibrium
  • Familiarity with free body diagrams
  • Basic principles of mechanics involving tension in ropes
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  • Study the principles of static equilibrium in detail
  • Learn how to draw and analyze free body diagrams
  • Explore the concept of normal forces in various mechanical systems
  • Investigate tension calculations in more complex systems involving multiple forces
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This discussion is beneficial for physics students, engineers, and anyone interested in understanding the mechanics of static systems and tension calculations in real-world applications.

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A ladder of length 2a and weight W, with its centre of gravity 3/8 of the way up it, stands on a smooth horizontal plane resting against a smooth vertical wall, and the middle point is tied to a point in the wall by a horizontal rope of length b. Find the tension in the rope.
 
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1. "Smooth" means no friction between ladder and wall/floor.
2. Set up the equilibrium equations (all three of them).
Solve for the 2 unknown normal forces plus the tension
 
Draw a diagram of the situation. Since the system is in equilibrium, the sum of all forces is zero. In addition, there is no net torque about the center of mass either.

The surfaces are smooth, implying no frictional force, but there is a normal force from both the horizontal plane and the vertical wall.
 

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