Good scales have equal arms (arms are the the things that connect the actual scale to the center), but in one grocery stall, the arms of the scale are not equal. Pending replacement, the manager wonders if he can give correct weight this way:
"I'll balance a 1-pound weight on the left with sugar on the right, and then I'll balance the 1-pound weight on the right with some more sugar on the left, and the sugar will add up to exactly 2 pounds."
Will it? What are other (assuming that the above works, it may not) ways of weighing 2 pounds of sugar, if you also have a lead shot with you to help weigh? (Note and hint: The lead shot has an unknown weight. You can make it whatever weight you choose. Remember, the arms aren't equal, and you need 2 pounds of sugar.)
The manager presumably has a set of weights. Put a 5-pound weight on the short side of the scale and "measure" its weight by placing smaller weights on the longer side. It will "measure" less than 5 pounds, so the 5-pound weight will not be needed to do the "measuring". This will calibrate the scale. (In fact, use the largest weight you have on the short side of the scale, to get the most fine calibration.)
In the case that you used the 5-pound weight, "measure" out 2/5 of whatever that "weight" of sugar, and you will actually have 2 pounds.
You could also figure the ratio of the lengths of the arms by first "weighing" the lead shot (or anything else) on one of the pans, and then on the other. The square root of the ratio of the "weights" will be the ratio of the lengths, which can then be used as a factor in decreasing or increasing the measured weight of the sugar.
Edited on May 23, 2004, 10:26 am
Posted by Charlie
on 2004-05-23 10:25:21