Understanding the Member Fixed to Collar on Smooth Rod Connection

[Cyrus]

I was reviewing my book when I got to thinking about a special type of connection, the "member fixed connected to collar on smooth rod" It prevents a force in the direction normal to the rod, and also prevents a moment. The first part is fine, but the moment part worried me a little bit. Since only a normal force can be prevented, any forces along the direction of the collar will make the collar move! So I was a little worried how it would prevent the moment caused by other forces to sum to zero. Here is the only explanation I could think of:

In order to prevent the external moments, a counter moment must be produced somehow. I thought it might be produced internally, but that does not seem to make much sense. How could an "internal" moment of the structure the collar is a part of prevent the external moments. So I thought about the problem locally to the collar. In actuality, the collar is "loose." This is what allows it to slide up and down. Since it is loose, when it is in static equilibirium and there is an external torque, the only place a counter torque can be produced is where the collar meets the rod. Keeping in mind that it is loose, it will actually contact the rod in two locations opposite to each other. (as shown in the diagram). So these TWO forces CAN produce the counter moment needed so the sum of the moments equals to zero. In addition, one of the forces has to be larger in magnitude than the other. By doing so, you still get the same amount of counter torque, and the difference between the two torques should equal the net force in the normal direction. In this way, it is possible to determine the TWO normal forces that are REALLY occurring. The book says 1 normal force, but I do not think that's very accurate. If my reasoning is wrong please let me know.

You can see in the picture that I made F' bigger than F in the right side. The difference F'-F should equal the F on the LEFT side. Also, the moment created by F and F'-(F'-F) the distance between them on the collar on the right pic, should equal the moment on the Left side (it should be obvious that the distance between the couple forces is the distance of the collar used, because the normal forces will always act in pairs on the ends of the collar). So this is the underlying reason why a counter moment can be produced.

Thanks, Cyrus.

 

[Greg Bernhardt]

Your explanation makes a lot of sense and it is helpful in understanding how the collar can prevent a moment. You have a great understanding of the physics behind this concept, and your diagram was very clarifying as well.