Solve Static Equilibrium: Beam, 520N Force, Cable Tension

In summary, the vertical beam is held up by a cable and is tensioned. The tension in the cable is calculated to be 520N. The reaction forces on the beam by the ground are not calculated.
  • #1
MPat
15
1

Homework Statement


A uniform vertical beam of mass 40kg is acted on by a horizontal force of 520N at its top and is held, in the vertical position, by a cable as shown.
a) Draw a free body diagram for the beam, clearly labelling all the forces acting on it
b) Calculate the tension in the cable.
c) Determine the reaction forces acting on the beam by the ground.

Homework Equations



ΣFx = 0

ΣFy = 0

Στ = 0

The Attempt at a Solution


a) I can't seem to add images to this. Whenever I try it only gives me the option of adding an image url which I don't have. Maybe someone can tell me how to do that!

For the image provided the uniform beam is standing up right (height of 5m). Force applied (520 N) acts on the top end of the beam to the left. A cable attaches the beam from 3m height down to the ground on the right. The angle between the ground and the cable is 28degrees.

In my free-body diagram I have the following forces acting on the beam.
Fa = 520N
Force tension from the cable
mg
Fn

Am I missing a force here? Should there be a force of friction between the beam and the ground? The question does not explicitly state anything about that.

b)
ΣFx = Ftx - Fa = 0

ΣFy = Fn-mg-Fty=0

Στ = Fa * 2 = 0
where the axis is located where the cable attaches to the beam at 3m. Ft does not create a torque force as it acts at the axis, and mg and Fn also do not create a torque force as the act directly away from the axis

I get here and I realize something is missing...based on the torque equation Fa would = 0, but Fa is given as 520N. Here's where I'm confused.

Please help!

Thanks
 
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  • #2
To add an image, you can try putting your image in a Word document, say, and then "cut" the image from the document and "paste" the image into your post. Or, when entering a post, you should see an "upload" button that you can use to upload a picture that is stored as a file on your computer.

You can see that your torque equation leads to a contradiction. So, maybe you were on the right track when you were wondering if friction between the beam and the ground should be included. Note that the question asks for the reaction forces on the beam by the ground.
 
  • #3
Use the upload button then the insert thumbnail or full size.
 

Related to Solve Static Equilibrium: Beam, 520N Force, Cable Tension

1. What is static equilibrium?

Static equilibrium is a state in which all forces acting on an object are balanced, resulting in no net acceleration or movement of the object.

2. How do you solve for static equilibrium?

To solve for static equilibrium, you must first identify all the forces acting on the object and their directions. Then, using Newton's Second Law (ΣF = ma) and the fact that the object is not accelerating, you can set up and solve a system of equations to find the unknown forces.

3. What is a beam in relation to static equilibrium?

A beam is a long, rigid object that is supported at two or more points and can carry loads along its length. Beams are often used in structural engineering and can be analyzed using static equilibrium principles.

4. What is the significance of a 520N force in this problem?

The 520N force is likely one of the external forces acting on the beam. By including this force in the analysis, we can determine the other unknown forces (such as the cable tension) that are necessary to maintain static equilibrium.

5. How does cable tension affect static equilibrium in this problem?

Cable tension is an internal force that can affect the overall stability and balance of the beam. In this problem, the cable tension must be strong enough to counteract the 520N external force and maintain static equilibrium.

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