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

In summary, the problem involves a metal pole with a mass of 10kg and a load with a mass of 50kg. The rope is attached at a point that is ¼ of the pole's length from the free end. Using a vector diagram with the origin at the hinge point, the equations \sum \tau=0 and \sum Fy = 0 are used to find the tension in the rope and the force at the hinge. The calculated values for tension, Ay, and Ax are 188.29 N, 523.7 N, and 176.93 N, respectively.
  • #1
lightonahill7
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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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  • #2
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.

[tex]\sum[/tex] [tex]\tau[/tex]=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:

[tex]\sum[/tex] Fy = 0

Ay - 98 - 490 + 188.29sin20 = 0

Ay = 523.7 N

[tex]\sum[/tex] Fx = 0

Ax - 188.29cos20 = 0

Ax = 176.93 N

Am I on the right track?
 

1. What is static equilibrium?

Static equilibrium is a state in which an object is at rest and all forces acting on it are balanced. This means that there is no acceleration or movement in any direction.

2. How do you calculate static equilibrium?

To calculate static equilibrium, you need to determine the sum of all the forces acting on the object (known as the net force) and the sum of all the torques (rotational forces) acting on the object. If both of these values are equal to zero, then the object is in static equilibrium.

3. What are the conditions for static equilibrium?

The conditions for static equilibrium are that the net force acting on the object must be equal to zero and the net torque acting on the object must also be equal to zero. This means that the object is not moving or rotating, as all forces and torques are balanced.

4. How does static equilibrium relate to stability?

In static equilibrium, an object is considered to be stable because it is not moving or rotating. If any external force or torque is applied to the object, it will still remain in its original position due to the balanced forces and torques.

5. What real-life examples demonstrate static equilibrium?

Examples of static equilibrium in everyday life include a book resting on a table, a ladder leaning against a wall, or a statue standing on its own. In all of these cases, the object is not moving or rotating, and the forces and torques are balanced.

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