Force acting upon three supports

[Xyius]

Homework Statement

A stick of mass M is held up by supports at each end, with each support providing a force of Mg/2.

Now put another support somewhere in the middle, say at "a" distance from one support and "b" distance from another.

What forces do the three supports now provide? Is it solvable?

Homework Equations

Newtons Laws

The Attempt at a Solution

Here is an image of my scanned work. (The top problem I am fairly certain I have correct, It wanted me to find the ratio of Jupiters escape velocity compared to Earths. So just ignore that one. Look at problem number 2!)

http://img64.imageshack.us/img64/9683/imgpbn.jpg

Basically I tried to find the mass of each section of the stick using linear density. Is this the wrong way to go about it? I feel like it is considering my professor is asking "is it solvable?"

Thanks!

 

[Spinnor]

Get a ruler and support it at the ends and then try and use your finger to support the ruler at some point near the middle. Depending on the precise vertical location of the middle support the load at the ends will vary. This is a problem that could be solved in an engineering mechanics class but not a first year physics class?

I think this is called an over constrained system?

 

[Xyius]

Well this class is actually called "Intermediate Mechanics" and its a few classes after the first mechanics.
I am still scratching my head on this one

 

[PhanthomJay]

Well this class is actually called "Intermediate Mechanics" and its a few classes after the first mechanics.
I am still scratching my head on this one

Have you studied statically indeterminate structures yet? There are more unknowns than there are equations of statics, so you must resort to other methods to solve this problem.

 

[Spinnor]

The question was asked of you "is it solvable"' I don't think the problem is unless you make some assumptions.

See

http://encyclopedia2.thefreedictionary.com/Statically+Indeterminate+System

Or

http://www.google.com/search?sclien...l25594l0l26596l32l31l0l19l0l0l241l241l2-1l1l0

 

[Spinnor]

If the stick had a pivot joint where the mid support was then you could solve the problem easily.

 

[PhanthomJay]

It us definitely solveable, it just requires a lot more work to do so, using deflection methods , for example, if the beam is flexible (aren't they all?) , and noting the fact that there is no displacement at any of the 3 supports.

 

[Xyius]

I have not studied statistically indeterminate structures yet, and I have not taken statics. But this homework isn't due for over a week and we have only had one class. I have yet to get the book (the book store doesn't have them in yet) but I am hoping we cover a problem like this in the time.

I just wanted to get the homework done as soon as possible. Even so, I don't even know how I would start this type of problem. (I will look into the links posted when I get a chance!)

 

[PhanthomJay]

Unless you assume a rigid beam on equally stiff supports, I don't know how you can solve this problem without a knowledge of statics, let alone without a knowledge of indeterminate analyses. What courses did you take??

 

[Xyius]

Unless you assume a rigid beam on equally stiff supports..

I am pretty sure that is exactly what I am supposed to assume. I do not think this is supposed to be an extremely complicated problem. This is the description of the course..

"Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations."

I have met all the pre-requisites as they are a few math courses and the first mechanics course so I do not think I am in need of knowledge I did not learn. Oh boy now I am REALLY scratching my head! haha

 

[PhanthomJay]

If the beam is rigid and the supports are of equal stiffness, the load is shared equally amongst the supports. Which still requires the knowledge of statics and Newton's first law of translational and rotational motion.

 

[Xyius]

I am going to go out on limb and guess that this problem isn't solvable which is why she is asking that in the original question. My question is, how would you set it up to show that it isn't solvable? Sum the forces on each support?

I do have some knowledge of statics as I used to tutor math and Physics at my old community college and sometimes strike up conversations with the people taking statics.

 

[PhanthomJay]

I am going to go out on limb and guess that this problem isn't solvable which is why she is asking that in the original question. My question is, how would you set it up to show that it isn't solvable? Sum the forces on each support?

I do have some knowledge of statics as I used to tutor math and Physics at my old community college and sometimes strike up conversations with the people taking statics.

1. The beam is solveable if it is rigid on equally stiff supports, in which case the reactions are each mg/3.
2. The beam is solveable if it is flexible on near rigid supports, in which case, for a = b, the left and right reactions are
each 3mg/16. and the middle reaction is 5mg/8. see

http://www.awc.org/pdf/DA6-BeamFormulas.pdf

3. If the beam is rigid on rigid supports, there is no solution.

In absence of other info, case 2 is usually assumed, but you would not be expected to know that. So is it solveable?? Your call.

 

[Xyius]

What do you mean by "equally stiff"? What is the difference between scenario 1 and 3? Would the reactions still be mg/3 even if a is not equal to b? How would I go about showing this?

I am assuming that my professor is referring to scenario 3 so I am going to go with it is not solvable. I just don't know how to show it other than summing the forces of each point where the supports are and showing that there are too many unknowns.

Just out of curiosity, how can it be not solvable? Shouldn't there exist a solution since the reactions DO occur and are each producing some sort of force? Or do you mean its not solvable without going into more advanced topics?

Thanks!

 

[PhanthomJay]

I believe this problem is becoming more and more complex than was intended, but this is what happens when a problem is underspecified.

What do you mean by "equally stiff"?

By that, I mean each elastic support will deform (compress) the same amount under the same load, that is, they have the same effective 'spring' constant, k.

What is the difference between scenario 1 and 3?

Scenario 1 is a rigid beam on elastic supports. Scenario 3 is a rigid beam on rigid supports.

Would the reactions still be mg/3 even if a is not equal to b?

For scenario 1, yes.

How would I go about showing this?

The supports deflect equally under the rigid beam's weight , and thus, the force in the supports must be equal. If the forces in the supports are not equal, then the the compressions of each support would not be equal (visualize the beam rotating about the left support, causing greater compression and thus greater load on the right support than the middle support), and equilibrium cannot be maintained, making such rotation and unequal compressions of the supports not possible, for supports of the same 'spring constant'.

I am assuming that my professor is referring to scenario 3 so I am going to go with it is not solvable. I just don't know how to show it other than summing the forces of each point where the supports are and showing that there are too many unknowns.

I guess that's what Spinnor said a few posts ago..the problem is not solveable unless you make some assumptions.

Just out of curiosity, how can it be not solvable? Shouldn't there exist a solution since the reactions DO occur and are each producing some sort of force? Or do you mean its not solvable without going into more advanced topics?

For scenario 3, I meant to say that there are an infinite number of solutions, and thus no specific solution, as long as the equations of equilibrium are satisfied. For example, the left and right supports might have a force reaction of mg/2 each, and the middle support reaction be 0. Or all support forces could be mg/3. Or 0 at the left and right supports, mg at the center support. They all satisfy equilibrium. For scenario 1 and 2, there is a specific solution as noted. But for case 3, you get into infinities...yes, the reactions do produce some sort of force in the real world, but it depends on what is happening in real life...completely rigid beams and rigid supports do not exist in our Universe.

Thanks!

You sure?

 

[Xyius]

Okay I completely understand now. Thanks so much! (Yes I am sure! :p)