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Proportional Weights

Date: 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
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Associated Topics:
Middle School Ratio and Proportion

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