Concept Overview
Quasi-equilibrium of forces on an extended body
Lecturer Procedure
| Steps to Follow | Expected Result |
|---|---|
| Yo-yo will first move away, and then stop. On second tug, yo-yo will move toward you. |
| On the first pull, the yo-yo will move toward you. On the second pull, the yo-yo will also move toward you. |
Historical References; Taken from original work of Percy H. Carr, 1970
“Place spoll [sic] on the lecture table so that it can roll with its cord coming off the under [sic] side of the shaft. Tell the students you intend to pull on the cord roughly horizontally and ask for their opinion. Four categories should suffice.
- How many think the spool will go away from you winding up the cord as it comes?
- How many think the spool will go away from you unwinding the cord as it goes?
- How many think something different than either of these will happen?
- How many don’t think?
Pull the cord gently. The spool comes to you winding up cord. show [sic] next that by pulling the cord quite steeply upward the spool will roll
away and unwind the cord. Argue there must be some angle for the cord in between those demonstrated for which there would be no rotation. Pull gently in a vertically upward direction and as the cord angle flattens by the receding of the spool, the spool will stop rolling at the critical angle; you can then move your hand horizontally and the spool will slide on the table maintaining the same position relative to the hand. Then explain. Draw the free body force diagram. Choose the contact point of spool on table as the axis for considering moments. Why? Because the moments of three of the forces is then zero, --even though the magnitude of friction is unknown. At this point it is easily seen that the direction of impending roll is determined by the line of action of the cord, the critical case occurring when this line also passes through the axis through the contact point.
Previously, this demo included a tapered block with a cord attached below the center of gravity. “Ask for opinion again as to what will happen if you pull horizontally on the cord. As before you will get a variety of answers. Then demonstrate. (It may be necessary to stand the block on a piece of sandpaper taped to the table to get enough friction at the base). The block falls toward the direction of pull. No need to go through the complete analysis again. Point out that thee force diagram for this is exactly the same as for the spool. In fact, just lop off the front and rear bulges of the spool and you have a towering column, and the bulges, not being in contact with anything, play no part in the picture of
what is impending.”
Video Demonstration
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