Torque and rotational equilibrium question

[Redwall54]

Homework Statement

8. A 20 kg uniform beam 10m long is attached to a wall with a cable. The cable is attached to the middle of the beam at a 90 degree angle to the beam. A box of mass 5 kg is also suspended from the beam. In addition to this, the beam is attached to the hinge at the bottom.

Solve for:

Tension in cable and total force acting on the hinge.

Homework Equations

Torque = Force * Distance

The Attempt at a Solution

So, I was able to determine the tension in the cable by finding the magnitude of all the forces in a perpendicular direction to the beam, then used those perpendicular forces multiplied by their distance to the hinge in a torque equation to determine the tension in the cable. However, I am completely stumped as to how I would determine the force acting upon the hinge. I would imagine that the whole system is in equilibrium and is unmoving (as this in on a section related to torque and rotational equilibrium), so I think the trouble that I'm having here is figuring out exactly what forces are acting on the hinge, and why they are doing so.

 

[TomHart]

Welcome to Physics Forums. The physical configuration was not real clear to me from the description. Is this what it looks like?

:)

 

[kuruman]

Generally there are two components to the hinge force, one horizontal and one vertical. Their values are whatever is necessary to keep the beam in equilibrium.

 

[Redwall54]

sorry about that, here is a full picture of the diagram and this is all the relevant info it gives me

 

[TomHart]

Kuruman gave a very good tip above in post #3. And for some of these types of problems - although I haven't attempted this one yet - I find it easier to break it down into x and y components, where the x and y are horizontal and vertical directions.

 

[Redwall54]

Generally there are two components to the hinge force, one horizontal and one vertical. Their values are whatever is necessary to keep the beam in equilibrium.

I see, so how would I relate that to the tension in the cable? Or does the tension of the cable not matter for this problem? I think that the main problem I'm having is actually figuring out WHICH forces apply to the hinge. My initial attempt at solving this question involved finding the total force of gravity present and then, using my known angles, finding the hypotenuse (which is in this case the beam), as I I'd thought that the only force that is actually present on the hinge would be the beam itself. This didn't result in me finding the right answer though, as I am once again stumped

 

[TomHart]

In this problem, in order for the beam to be in equilibrium, the sum of all of the forces must equal 0. Typically, one would break down forces into x and y components (horizontal and vertical components), and then sum the forces in the x direction to equal 0, and sum the forces in the y direction to equal 0. So in this problem, can you identify all of the components in the x direction. I think it is fairly obvious that the tension force has a component in the x direction (specifically in the negative x direction). So there must be at least 1 other force (possibly more) in the x direction to counter the x component of the tension force so that all of the x forces sum to 0.