How Do You Calculate Tension and Reaction Forces in a Leaning Broom Problem?

[ultrapowerpie]

Homework Statement

Image of problem: http://img227.imageshack.us/my.php?image=physics3ue4.png

A 1229.0 N uniform broom of length L is supported by a cable. The broom is pivoted at the bottom, the cable is attached a distance (3/4)L from the pivot, and a 2442.0 N weight hangs from the brooms top.

I need to find the Reaction forces (vertical and horizontal), as well as the tension.

Homework Equations

The basic statics equations, Sum of Moment and Force = 0

Moment = Torque= r x F

The Attempt at a Solution

This is more a problem of setting up this equation. I'm perfectly fine at solving Statics equations, but it's setting them up that I have dificulties with. Here's my questions:

1) Ok, I'm looking at 4 variables, and three equations. I don't know L, don't know the reaction forces, and the Tension. In statics, this would technically be "statically indeterminte" because we only have two force equations and one moment equation. The problem here is that since L is unknown, and I have to input a number.

2) How does the broom's angle play into all of this. I know it plays a factor, but for the life of me, I can't figure out where to apply that angle too. >.>

Thanks in advance.

 

[PhanthomJay]

Homework Statement

Image of problem: http://img227.imageshack.us/my.php?image=physics3ue4.png

A 1229.0 N uniform broom of length L is supported by a cable. The broom is pivoted at the bottom, the cable is attached a distance (3/4)L from the pivot, and a 2442.0 N weight hangs from the brooms top.

I need to find the Reaction forces (vertical and horizontal), as well as the tension.

Homework Equations

The basic statics equations, Sum of Moment and Force = 0

Moment = Torque= r x F

The Attempt at a Solution

This is more a problem of setting up this equation. I'm perfectly fine at solving Statics equations, but it's setting them up that I have dificulties with. Here's my questions:

1) Ok, I'm looking at 4 variables, and three equations. I don't know L, don't know the reaction forces, and the Tension. In statics, this would technically be "statically indeterminte" because we only have two force equations and one moment equation. The problem here is that since L is unknown, and I have to input a number.

2) How does the broom's angle play into all of this. I know it plays a factor, but for the life of me, I can't figure out where to apply that angle too. >.>

Thanks in advance.

You may not neeed to know the exact value of L. Sum torques about the base of the boom to solve for T. You'll need to know the angles before you can correctly determine the torques.

 

[thomate1]

I would approach this problem by first identifying the known and unknown variables and then setting up the appropriate equations to solve for the unknowns. In this case, the known variables are the weight of the broom (1229.0 N), the weight hanging from the top (2442.0 N), and the distance from the pivot to the cable (3/4 L). The unknown variables are the length of the broom (L), the reaction forces (vertical and horizontal), and the tension in the cable.

To set up the equations, we can use the principles of statics - specifically, the sum of forces and moments equal to zero. Since the broom is in equilibrium, the sum of forces in the vertical and horizontal directions must equal zero. This means that the vertical reaction force must equal the weight of the broom plus the weight hanging from the top. The horizontal reaction force must equal the tension in the cable.

To determine the moment equation, we first need to choose a pivot point. In this case, the pivot point can be at the bottom of the broom since it is fixed. We can then use the principle of moments, which states that the sum of moments about any point must equal zero. This means that the moment created by the weight hanging from the top must be balanced by the moment created by the tension in the cable.

To incorporate the angle of the broom, we can use trigonometry to determine the components of the weight hanging from the top in the vertical and horizontal directions. We can then use these components in our equations to solve for the unknown variables.

In summary, the key to solving this problem is to identify the known and unknown variables, set up the appropriate equations based on the principles of statics, and use trigonometry to incorporate the angle of the broom. I hope this helps you in solving the problem successfully.