lew@ihuxr.UUCP (10/03/83)
You have to really BELIEVE Newton's second law for this one. Take the hourglass (including sand) as a system. The sum of the external forces equals the acceleration of its center of mass. While the hourglass is running its center of mass has a constant velocity. There is a short downward acceleration as it starts and a short upward acceleration as it stops. This means that it will "weigh light" for a moment as it starts, and conversely. When it weighs light, the vector sum of its weight (force of earth on hourglass) and the force of the scale on the hourglass will be in the downward direction. Note that if you regard the top chamber as a "rocket", it has zero thrust becuse of a zero exhaust velocity. The impact at the bottom is just great enough to account for the "missing mass" of the sand in freefall: V*(dm/dt) = (dm/dt)*T * g since V=g*T During startup, the net force on the hourglass increases linearly from 0 to (dm/dt)*T*g during the time T that the sand takes to fall, then drops to zero abruptly as the sand begins to hit bottom. The same thing occurs as the sand runs out, except the force is in the opposite direction. With dm/dt ~ 1gram/minute and g*T = V ~ sqrt(2*1000 cm/sec2 * 5cm) = 100 cm/sec, I estimate a peak force of about 1 dyne. That's about .001 gram-force. Pretty subtle, but you should be able to measure it with the right scale. I tried once on a crude balance with no success. Of course, you have to try for the heavy spike as it stops, as a practical matter. Lew Mammel, Jr. ihuxr!lew
bnp@ihldt.UUCP (10/04/83)
I think I have seen a problem similiar to this one; in high school physics our teacher used to give "demonstration problems" during exams. When there was about 15 minutes left in the class period, he would get everyone's attention, perform a demonstration similiar to (but always a little more difficult than) one we had seen and explained in class. As the final question on the test, we would have to qualitatively explain what happened in the demonstration. Anyway... One of these demonstrations consisted of a balance with a yo-yo tied to one side, and static weights equalling the mass of the yo-yo on the other side. He then would wind the yo-yo string and released it. As it fell and then rose again, the balance would show first one side as "heavier", and then the other. As I recall, the balance "switched" as the yo-yo reached the bottom of its string. Still a little confused...., Bruce Peters BTL - Naperville, Ill. ...!ihnp4!ihldt!bnp