PROBLEM OF THE BALANCE
By Preston Q. Boomer
Solved by Jearl Walker
Tested by SLVHS Physics Students
Ah, we are about to learn something that very few people know!
BACKGROUND:
For many years, The Boom wondered why an object, say a meter stick, will balance horizontally. A force is needed to rotate the stick a few degrees, and when the stick is released, it returns to the horizontal. Why?
When the balanced meter stick is turned somewhat, one end is closer to the earth by a few centimeters and should therefore be ever so slightly heavier, while the other end, being a few centimeters farther from the earth, should be somewhat lighter. This torque will tend to keep the stick turning toward the vertical, and not return it to horizontal balance.
Also, when the meter stick is rotated, its center of gravity is shifted to one side of the fulcrum, and this torque should encourage the stick to continue rotating to the vertical.
Over the years, The Boom has asked knowledgeable people about this and received the same answer, "Gee, I don't know, I never thought about it before."
After reading an anthology of Isaac Asimov articles, The Boom wrote to him and received a nice reply on 9/7/76, in which he stated, "I am but an amateur physicist but it seems to me that torque depends on weight and distance from fulcrum, If the bar tilts, horizontal distance from fulcrum decreases and torque moves back to maximum--- but I may be all wrong."
In May, 1987, The Boom re-read his copy of FLYING CIRCUS OF PHYSICS by Jearl Walker (who also is editor of THE AMATEUR SCIENTIST in SCIENTIFIC AMERICAN), and noticed that in it he invites questions. The Boom sent him the problem, and immediately received an enthusiastic answer. He said that he didn't known either, but he proposed the following explanation:
"It must be that the fulcrum is not microscopically sharp. Instead, it must have a slightly flat top, although it may look sharp to the unaided eye. When you lower the right side, the stick actually pivots around the right side of the flat top, with the center of mass always slightly to the left of that pivot. When you then release the stick, gravity pulls on the center of mass, causing a torque that returns the stick to the horizontal. This action by gravity overwhelms the slight difference in the weight of the two halves of the stick when the stick is released."
So we clamped a razor blade in a vice and attempted to balance a meter stick on it. After 15 frustrating minutes, we gave it up. We could not balance the stick on a super sharp fulcrum (where the shift of the fulcrum to a new fulcrum would by negligible).
We then we tried it with kilogram masses hanging at each end of the meter stick. At first it was easy to balance, but then we noticed quite a bend in the stick due to the heavy weights. So we turned the stick onto its narrow edge to reduce bending. We were unable to balance it. We would get very close, but never succeeded in having it balance for more than a few seconds.