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Re: Train Physics Problem

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On 11/2/2015 8:05 PM, Fabian Russell wrote:
> Attention physics enthusiasts:
>
> In all of the information that I have encountered about train
> physics -- and there is not a lot of material available -- the
> energy required to move a train is calculated by considering
> factors such a inertia (train mass), mechanical resistance (friction),
> and air resistance (drag).
>
> However, one significant factor is always ignored, and that is
> the rotational energy of the wheel sets.
>
> Why?  What is the reason for omitting the rotational energy?
>
> In the US, a train wheel is very nearly 1 meter in diameter and
> has a mass of 1000 kg.  The rotational energy for one wheel is
> then 1/2 * I * w^2.  At 60 mph (27 m/s) speed, the energy is 179862 Joules.
>
> At 4 wheel sets per car (8 wheels) with an average train containing
> 100 cars, the total rotational energy of the wheels is a whopping
> 143889600 Joules = 144 megajoules.
>
> Yet this energy is ignored.

I don't know that it's ignored, but let's put those large numbers in 
perspective.

Let's compare the rotational kinetic energy of the wheels to the 
translational kinetic energy of the wheels.
w = v/r, and for a disk wheel, I = (1/2)m*r^2.
So the rotational KE = (1/2)(1/2)m*r^2 * (v/r)^2 = (1/4)mv^2. The 
rotational KE of the wheels is thus half the translational KE of the wheels.

Now we can compare the translational kinetic energy of the wheels to the 
translational kinetic energy of the train as a whole.

As you say, 800 wheels on a 100-car train has a mass of about 800 metric 
tons. But the mass of a fully loaded train is about 10,000 metric tons. 
So the translational kinetic energy of the wheels is about 8% of the 
train's translational kinetic energy, and the rotational kinetic energy 
of the wheels is then about 4% of the train's total kinetic energy.

Not insignificant, but not huge either.

>
> For a reference, see page 2 of this link:
>
> http://s000.tinyupload.com/?file_id=07666111176590991515
>
> This is a Microsoft Word (doc) file.
>
> A LibreOffice (odt) version is here:
>
> http://s000.tinyupload.com/?file_id=00684379287173743496
>


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:05 +0000
  Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:31 +0000
    Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:38 +0000
    Re: Train Physics Problem gillyshin <spectrum8@sincity.info> - 2015-11-03 04:38 +0000
      Re: Train Physics Problem gilber34 <fafa@invalid.com> - 2015-11-02 22:58 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 05:22 +0000
  Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 08:38 -0600
    Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 18:19 +0000
      Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 15:00 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:22 +0000
          Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 16:55 -0600
            Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 23:19 +0000
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:31 +0000
          Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 17:17 -0600
    Re: Train Physics Problem benj <none@gmail.com> - 2015-11-03 13:41 -0500
      Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 18:53 +0000
        Re: Train Physics Problem benj <none@gmail.com> - 2015-11-04 18:08 -0500
          Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-04 23:33 +0000
      Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 15:10 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:48 +0000
          Re: Train Physics Problem benj <nobody@gmail.com> - 2015-11-04 02:45 -0500
  Re: Train Physics Problem "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-11-03 09:19 -0800
    Re: Train Physics Problem "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-11-04 15:15 -0800

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