Math Problem Statement
Solution
The question is about identifying the correct direction of the force on the rod at point X due to the torque, considering the rod is hinged at point X and held horizontally by a cable.
Explanation
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Torque Analysis: The rod is supported at point X and held by a cable on the other end. Since the cable applies a force vertically (downward tension force), the torque around point X due to the rod's weight will cause it to rotate downwards around the hinge at point X.
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Force Direction at Point X: The force at the hinge (point X) must counteract this torque and maintain equilibrium. This force will generally act upwards and to the left at an angle to counterbalance both the vertical force due to the weight of the rod and any horizontal force component due to the cable tension.
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Correct Answer: Looking at the options provided in the figure, the arrow that represents this force's direction is Arrow B. Arrow B points up and slightly to the left, which aligns with the expected direction for balancing the forces in this setup.
Answer
The correct answer is: Arrow B
Would you like more details on the torque calculation or the equilibrium conditions?
Here are five related questions for deeper understanding:
- What is the torque generated by the rod's weight about point X?
- How does changing the angle of the cable affect the direction of the force at point X?
- What role does the rod's weight distribution play in determining the force direction at point X?
- How would the force direction at point X change if the rod were not uniform?
- How can we calculate the exact magnitude of the forces acting at point X?
Tip: Understanding torque in static equilibrium is essential when analyzing forces in systems with hinges or pivots.
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Math Problem Analysis
Mathematical Concepts
Static Equilibrium
Forces and Torques
Vector Analysis
Formulas
Torque = Force × Distance
Equilibrium condition: ΣF = 0, Στ = 0
Theorems
Equilibrium of Forces and Moments
Suitable Grade Level
Grades 10-12
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