2-Dimensional Torque problem involving two torque points.

[Ascendant78]

Homework Statement

Homework Equations

The Attempt at a Solution

Excuse me for the large images. I figured it would be easier than re-writing it all and wanted to show what I've been doing. I know my work isn't too clear, but in short, I haven't dealt with a problem involving two torque points like this yet and am not sure how to deal with it. I attempted to analyze each pillar separately to find how much force the opposite pillar would have to apply to keep the scaffold stationary (no angular acceleration). My result was 1269N for one and 446N for the other, but the answers in the back are 1117N for one and 9.8N for the other, so clearly I'm doing something seriously wrong.

If someone can just point me in the right direction as to what I need to do in order to analyze a torque problem like this involving two torque points, I would greatly appreciate it.

 

[SteamKing]

The answers you give for the solution of the problem (the back of the book numbers) of 1117 N and 9.8 N are clearly incorrect. You have 2 twins (70 kg each) and a 35 kg board, which is a total of 175 kg, or 1715 N, assuming g = 9.8 m/s^2. The sum of the reactions must equal 1715 N for the board to remain in static equilibrium. This sum clearly is greater than what the book says it should be.

Your problem statement is incomplete. If this is just a static equilibrium problem, there is no need to bring T = Ia into the solution. Is there more to the problem statement which you haven't posted?

 

[Ascendant78]

The answers you give for the solution of the problem (the back of the book numbers) of 1117 N and 9.8 N are clearly incorrect. You have 2 twins (70 kg each) and a 35 kg board, which is a total of 175 kg, or 1715 N, assuming g = 9.8 m/s^2. The sum of the reactions must equal 1715 N for the board to remain in static equilibrium. This sum clearly is greater than what the book says it should be.

Your problem statement is incomplete. If this is just a static equilibrium problem, there is no need to bring T = Ia into the solution. Is there more to the problem statement which you haven't posted?

Well, just got an e-mail back from my professor about this one. Apparently, there was a typo in the solutions and the answers to two consecutive problems were flip-flopped. The ones I gave were actually the correct ones and the ones given in the book were wrong.

As far as the ambiguity of the problem, it happens a lot in this book we use (Spiral Physics). To be honest, though I managed to get the correct answers to this problem, I am not quite sure how I would go about determining if the torque on either side would be enough to cause a lift or not. So, I just went with the assumption that there was no lift since it didn't indicate that there was in the problem.

Anyway, thanks for responding and apologies about the confusion.

 

[SteamKing]

If you want to determine if the board lifts off from one support or the other, this can still be accomplished using an ordinary static analysis. The reactions in the supports would normally be taken to act in the positive (upward) direction. If your static analysis determined that one of the reactions would have to be negative in order to keep the board in static equilibrium, then you have also determined that the board would lift off.

 

[Ascendant78]

If you want to determine if the board lifts off from one support or the other, this can still be accomplished using an ordinary static analysis. The reactions in the supports would normally be taken to act in the positive (upward) direction. If your static analysis determined that one of the reactions would have to be negative in order to keep the board in static equilibrium, then you have also determined that the board would lift off.

Oh, thank you! That makes perfect sense and is actually easier than I thought it might be.

I'm still working on grasping all this because our professor never got to this section of the book. Long story short, the slow students held our class schedule back severely. I'm not too happy that I'm now having to teach it to myself over my break instead of some other things I wanted to get to. Anyway, I really appreciate the information.