Mathematics and Society - OS X Lion Server

PLANKMaterials Needed:Long plank about 3 metres long, concrete building block, bathroomscale, measuring tape, metre stickI. Balance the plank by placing the block in the middle. Ask for a volunteer (orthe teacher) to stand on one end of the plank. Have different members of theclass try to balance the plank by standing on the opposite end. For the plankto balance students should realize the weights of the volunteers should be aboutequal. Weigh the volunteers.II. Pick two members of the class having different weights. Weigh them and recordthe weights. Keep the block in the middle and ask them to stand on oppositehalves of the plank and balance each other. Students will probably use theirprevious experience with teeter-totters to accomplish the task.III. Again pick two members of the class having different weights. This time theirtask is to move the block so the plank will balance with one of them on eitherend.IV.Have the students use the three activities above to formulate a conjecture abouthow to make unequal weights balance. Students will probably say that the heavierweight is closer to the block, and the lighter weight is farther away from theblock.V. Ask students to examine the relationship between the weights and distances bycompleting a table. By using two students whose weights are considerably different,a pattern can be discovered. The results in the last column will beapproximately equal.Wei9ht of'Dista.nce wis froCI)) W+D W-D W+D \'vxDoel"son(w) blockDThe Genero.l Ru.le is : WI D... -- =--.W l D.VI. Students can apply the general rule to solve problems: For example, John has amass of 40 kg and stands 1.5 metres from the block. Tim balances the plank bystanding 2 metres from the block. How much does Tim weigh?"Give me a place to stand, and I will move the Earth."This is what the famous Greek scientist Archimedes (287­212 B.C.) was supposed to have boasted after discoveringthe law of the lever: WI x D I= w 2x D 2. Assume thatArchimedes weighs 150 lbs., and the fulcrum of the leveris 4,000 miles from the Earth. How far from the fulcrumwould he have to stand in order to move the Earth? TheEarth weighs 13,176 ,000, 000, 000, 000, 000., 000 ,000 lbs.339