Chapter 11: Problem 9
A 350-N, uniform, 1.50-m bar is suspended horizontally by two vertical cables at each end. Cable \(A\) can support a maximum tension of 500.0 N without breaking, and cable \(B\) can support up to 400.0 N. You want to place a small weight on this bar. (a) What is the heaviest weight you can put on without breaking either cable, and (b) where should you put this weight?
Short Answer
Step by step solution
Identify forces and moments
Set up equilibrium equations
Apply force equilibrium
Calculate moment about one end
Solve for tensions without exceeding limits
Solve system of equations
Calculate final values
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Torque
- The moment arm is the perpendicular distance from the pivot point to the line of action of the force.
- Torque is calculated as the force multiplied by the moment arm: \( \text{Torque} = \text{Force} \times \text{Distance} \).
- In this exercise, placing a weight on the bar introduces additional torque, which needs to be counterbalanced by the cables to prevent rotation.
Tension in Cables
- Each cable at the bar’s ends supports a portion of the total weight, including the weight of the bar itself and any additional weight added.
- The tension in the cables must not exceed their maximum capacity of 500 N for cable A and 400 N for cable B to prevent them from breaking.
Force Equilibrium
- For a system in equilibrium, the sum of all vertical forces acting on the bar must equal zero.
- This principle is applied in this scenario by ensuring that the tension in cables A and B, combined with the bar's and added weight's forces, equilibrate perfectly.
Statics
- Statics involves analyzing forces and torques acting on a body to determine conditions of equilibrium.
- Here, you must account for the forces from the bar's weight, the added weight, and the tension in cables to ensure the system is in a stable equilibrium.
Mechanical Equilibrium
- For the bar in the problem, achieving mechanical equilibrium means balancing all forces and torques so that neither end of the bar tilts up or down.
- By ensuring that both conditions of equilibrium are met, you can place the maximum weight possible without risking cable failure.