Amusing Problems
The See-Saw Scene
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Summer has arrived, and Dr. J gets as close to politics as his conscience will allow. He takes a position with the city government as parks inspector. It is time to fill out his first week's report with his recommendations. For example, what should be done about the continuing vandalism of the chain-link barrier surrounding softball field "D"? "Simple," writes Dr. J. "We will hire a security guard to serve as a miniature department of 'D' fence." Or how about the deteriorating condition of the playground equipment? It is so bad that people are inclined not to use the slides. Fewer and fewer are being swayed toward trying the swings. The worst problem for Dr. J, however, is getting the see-saw back into working condition. A large rock had fallen on one end, pinning it to the ground. Dr. J climbed to the other end and succeeded in moving the stubborn stone (he was trying to balance the budge-it), but the see-saw is still unbalanced. For one thing, the pivot point is 0.1 m off center. In addition, the seat on the long end has 20 extra bolts, each with a mass of 0.1 kg. Dr. J recommends fastening a 10 kg lead bar 1 m in length underneath the short side.
If the see-saw board is 7 m long and has a mass of 30 kg, how far from the short end should it be?
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