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

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SUMMARY

The discussion focuses on calculating tension and hinge forces in a static equilibrium scenario involving a metal pole and a load. The pole has a mass of 10 kg, and the load is 50 kg, with the rope attached ¼ of the pole's length from the free end. The calculated tension in the rope is 188.29 N, and the hinge forces are determined to be 523.7 N vertically and 176.93 N horizontally. The user employs torque equilibrium equations and vector diagrams to arrive at these values, confirming the correct approach to solving the problem.

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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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