Help with free body diagram

1. Feb 3, 2013

pyroknife

For the attached picture I need to draw a free body diagram for the structure supporting the pulley.

At the fixed end (left), there would be a vertical and horizontal reaction force as well as a moment.

I am not sure what the forces and moments would be for the part connected to the pulley. What would it look like for this situation?

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2. Feb 3, 2013

tms

You're shown some of the forces. What others are missing?

3. Feb 3, 2013

pyroknife

I did not show any forces in the picture.

There should be a force where the pulley is attached, but I don't know what direction that should be in.
Edit-I think there should be a reaction force where the pulley is connected in 'both' the x and y direction.

4. Feb 3, 2013

pyroknife

There should also be a reaction moment where it's connected.

5. Feb 3, 2013

tms

What about the string that runs over the pulley?

6. Feb 3, 2013

pyroknife

The 2 forces shown are given. They act on the pulley. The problem is to draw a free body diagram for the structure.

7. Feb 3, 2013

tms

Does the pulley exert any forces on the structure?

You've said the wall exerts a reaction force on the beam? What is it reacting to?

8. Feb 3, 2013

pyroknife

The wall holds the cantilever beam. It exerts a horizontal and vertical (maybe) force on the structure. It also exerts a moment because it's cantilevered.

The pulley is being held by the structure, so yes, it exerts a force which should be both in the horizontal and vertical direction. My question is if this is right and if there is a moment exerted as well.

9. Feb 3, 2013

Staff: Mentor

There is no moment at the pulley, because the pulley bearings prevent this. But there is a vertical force and a horizontal force exerted by the pulley axis (spindle) on the structure.

10. Feb 3, 2013

SammyS

Staff Emeritus
Yes, there is a moment.

Are the bracket holding the pulley, and the pulley itself massive enough so the their masses have to be considered?

11. Feb 3, 2013

pyroknife

Thank you.

It seems Chestermiller and SammyS may have conflicting opinions on whether there should be a moment exerted where the pulley is attached.

"Are the bracket holding the pulley, and the pulley itself massive enough so the their masses have to be considered?" I believe the structure is what's the pulley. I have as much info as you guys, so I'm not entirely sure. Typically for shear and moment diagram (which this is) problems, we ignore mass. This is what I assumed since they don't give you mass.

I think I agree with Chestermiller that there isn't a moment exerted at where the pullley is.

12. Feb 3, 2013

pyroknife

Attached is what I think the free body diagram should look like.

Where the 4 arrows indicate the arbitrary reaction forces and the counter clock wise arrow represents the moment.

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• Untitled.png
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13. Feb 3, 2013

SammyS

Staff Emeritus
There's a moment exerted at the junction of the structure and the wall. (I thought that's what the question was asking.)

14. Feb 3, 2013

pyroknife

Oh no, I mean where the pulley and structure were connected. It was a dumb question.

15. Feb 3, 2013

SammyS

Staff Emeritus
I agree that the two forces in the figure produce a zero moment about the pulley axis.

16. Feb 4, 2013

PhanthomJay

You have correctly shown the force and moment reactions at the fixed end, but at the pulley end, although you have correctly identified the 2 forces acting there, you have incorrectly shown the direction of those forces, and you have not indicated their magnitudes. Their direction and magnitudes must be properly shown on the FBD of the frame. The direction and magnitudes of the forces on the frame at the pulley can be determined by first drawing a FBD of the pulley, and then applying Newton's 3rd law.

When you talk about 'arbitrary' reaction forces and moment at the wall, I am not sure what you mean. You can arbitrarily choose their direction, I suppose, and their true directions will be determined when the equlibrium equations are applied. But their is no arbitation on their magnitudes (unknown until the equilibrium equations are applied), and no arbitration whatsoever in the magnitude and directions of the forces at the pulley end.

17. Feb 4, 2013

caldweab

If the reactions are drawn in the wrong direction, then their value will come out negative. The magnitude should still be the same. And don't say that a beam exerts a moment because its cantilever, it exerts a moment because the fixed support prevents it from wanting to rotate. What if the beam was supported by a roller or pin? Neither one of those supports have a moment reaction

18. Feb 4, 2013

Staff: Mentor

A beam with a roller or pin is not cantilevered. The definition of a cantilever beam is one that is "built in" (to a wall).