Proportional WeightsDate: 08/21/98 at 16:02:36 From: josue alvarado Subject: Proportional Weights Hello Dr. Math, This is my first time. Please try to help me. Jim weighs 60 kilograms and needs to lift 300 kilogram rock. His crowbar is 1.5 meters long. How close must the fulcrum be to the rock so that Jim's weight can lift the rock? Date: 08/22/98 at 16:40:12 From: Doctor Peterson Subject: Re: Proportional Weights Hi, Josue. This is an interesting kind of proportion question. I'm not sure what sort of math or physics you have been working in, so my method may not be what you are expected to do, but I think it's neat. To give you a chance to solve the problem yourself, I'll use different numbers. Let's say Jim weighs 50 kg, the rock is 200 kg, and the crowbar is 1.25 m long. What you need to know is that the distances that Jim and the rock are from the fulcrum have to be proportional to their weights. Since the ratio of their weights is 4:1, the ratio of their distances must also be 4:1: Jim Rock 50 kg 200 kg + + =========================================================== 4 ^ 1 (To put it another way, Jim's weight times his distance must equal the rock's weight times its distance.) So we have to divide the 1.25 m bar into 5 equal parts and put 4 on one side and 1 on the other. Since 1/5 of 1.25 m is 0.25 m, that is how far the rock has to be from the fulcrum. There are many ways to solve this problem, some using more algebra, others using proportions, but this way is about the simplest I know. - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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