How Do You Calculate Tension and Hinge Forces in Static Equilibrium?

AI Thread Summary
To calculate the tension and hinge forces in static equilibrium for a metal pole with a mass of 10kg and a load of 50kg, the tension in the rope was found to be approximately 188.29 N using torque equilibrium equations. The vector diagram was set with the origin at the hinge, and the torque equation was established with respect to the hinge point. The vertical force balance yielded an upward force at the hinge of 523.7 N, while the horizontal force balance resulted in a horizontal force of 176.93 N. The calculations appear to be correct based on the provided equations. This approach effectively determines the forces acting on the system in static equilibrium.
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Homework Statement



The metal pole has a mass of 10kg, and the load has a mass of 50kg. The rope is attached so that it is ¼ of the pole’s length from the free end of the pole. Find the tension in the rope and the force at the hinge.

Homework Equations





The Attempt at a Solution

 

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I have tried to set up this problem but would like some feedback.

I want to set my vector diagram with the origin placed at the hinge point, with y+ upwards and x+ going to the right.

\sum \tau=0

T(3/4)sin20 - 98N(1/2)sin50 - 490(1)sin50 = 0

T(3/4)sin20 = 412.8979548

T = 188.29 N

If I am right with the value for tension, then to find x and y components of force would be:

\sum Fy = 0

Ay - 98 - 490 + 188.29sin20 = 0

Ay = 523.7 N

\sum Fx = 0

Ax - 188.29cos20 = 0

Ax = 176.93 N

Am I on the right track?
 

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