Calculating Tension and Total Force in Equilibrium Torque System

AI Thread Summary
The discussion focuses on calculating the tension in a wire and the total force at a hinge for a uniform beam in equilibrium. The beam, measuring 5.00 m and weighing 2.00 x 10^3 kg, is analyzed using torque equations. The torque due to the beam's weight is calculated as 2000(9.8)(2.5)(cos20), while the torque from the tension is represented as T*sinθ*L. The calculations lead to two different tension values: 135426.28 N and 26926.87 N, indicating confusion in the application of torque principles. Clarification on the correct approach to torque and tension calculations is needed for accurate results.
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Homework Statement



Note Picture...

A uniform beam, 5.00 m long with a mass of 2.00 x 103 kg, is held against a wall in the position shown by a hinge and a horizontal steel wire attached to its end.



a) Find the tension in the wire.
b) Find the magnitude of the total force supplied by the hinge.




The Attempt at a Solution



the only forces for the torque is the mass of the beam perpendicular to the beam as well as the tension of the cable

beam torque = mgdcosQ = 2000(9.8)(2.5)(cos20)
tension torque = TxsinQ this is where I am a littel confused because the tension is in the x direction but the torque should be perpindicular to the beam so its confusing me.

2000(9.8)(2.5)(cos20) = TxsinQ...Tx = 135426.28

is this correct
T
 

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Torque due to the tension is T*sinθ*L where L is the length of the beam.
 
oh right right...

2000(9.8)(2.5)(cos20) = Tx(5)sin20...Tx = 26926.87 N

is this correct
 

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