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Massless Cable

Date: 05/06/2003 at 17:04:53
From: Jeremy
Subject: Massless cable.

Why is it that cables are always considered to be massless in a 
system?

My guess is that a cable can support weights around a wheel at both 
ends, so the mass of the cable is negligible or not important.


Date: 05/07/2003 at 11:47:34
From: Doctor Dotty
Subject: Re: Massless cable.

Hi Jeremy,

Thanks for the question.

When applying maths to the real world, we can often make our 
calculations easier by simplifying our description of the 
situation.  For that reason, mathematicians and physicists 
often ignore such factors as air resistance, the size of the 
tip of a fulcrum, the gravitational effect of Pluto, etc.

Let's say that you have a van being pulled by a rope:

    500 N             _ _ _ _  
     /_______________| 5 tons \_
     \               |_ _ _ _ _ _|
                       O     O

The 5 ton m ass is probably rounded to the nearest ton. 
The 500 Newton force is probably rounded to the nearest 
50 Newtons. We would take the acceleration due to gravity 
to be 9.8m/s^2, which is rounded to one decimal place. 

Let's say the van is about to move.

If you had to work out, for example, the coefficient of friction 
between the van and the ground, the answer would only be correct to 
a couple of decimal places because of this. The mass of the rope is 
so small when compared to the 5-ton van, that it would not affect 
this rounded answer at all.

Does that make sense? 

If I can help any more with this problem or any other, please write 
back!

- Doctor Dotty, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Physics/Chemistry

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