How Do You Calculate the Tension in a Cable Supporting a Boom at an Angle?

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To calculate the tension in the horizontal cable supporting a boom at an angle, it is essential to analyze the forces acting on the system. The mass of the boom and the suspended mass must be considered, along with the angle of the boom from the vertical. A diagram illustrating the forces and their components is crucial for understanding the static equilibrium conditions. The tension can be resolved into X and Y components, allowing for the application of force and torque equilibrium equations. Properly setting up these equations will lead to the solution for the tension in the cable.
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Homework Statement



2. A mass M=169 kg is suspended from the end of a uniform boom.The boom (mass=90.0 kg, length=3.60 m) is at an angle θ=68.0 deg from the vertical, and is supported at its mid-point by a horizontal cable and by a pivot at its base. Calculate the tension in the horizontal cable.



Homework Equations



T=mg
T=ma


The Attempt at a Solution



i am not sure how to solve for tension when given an angle. i know i need to use sin(68) somewhere in the problem i am just confused as to where
 
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This is again a static equilibrium problem. You need a review, I am afraid.
 
Can you draw the diagram confidently, showing all the forces? What are all the forces (magnitude, direction, line of action - use symbols for unknowns as necessary)? Do you know how to resolve a force at an angle into X and Y components? Can you then write the various force and torque equilibrium equations?
 

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