[boost] [Off Topic] Physics (was re: Boost Units library preview)

From: Dave Steffen (dgsteffen_at_[hidden])
Date: 2006-08-23 14:47:31

Andy Little writes:
[...]
 > 
 > The serious point was that there is a relation between torque and energy, but
 > they are distinct.
 >  and actually the relation is slightly more complicated than I stated, but I
 > think that for a bolt of N turns
 > and assuming a constant torque, the heat dissipated  (in Joules) ==
 > applied_torque (in N.m)  * N / (2 * pi).

 OK, hold on here.

 Work = change in energy = force * distance.

 (Actually, the integral of force * infinetesimal displacement, but
 let's assume constant forces here.)

 Torque = radius * Force.  (Actually, it's a cross product, but let's
 assume the force is always perpendicular to the lever arm.)

 Therefore, for a given torque, Force = Torque / radius.

 So, the work done (delta engergy) in applying a constant torque to
 your bolt is

    W = Force * distance = ( Torque * distance ) / radius.

 Now, if you turn the bolt N times, the distance you've moved the end
 of your lever arm (where you're applying the force) is 

   distance = 2 * pi * radius * N.
   
 Plugging this in, 

   W = (Torque * 2 * pi * radius * N) / radius

  or

 W = 2 * pi * N * Torque.

 [[ End of physics lesson ]]

----------------------------------------------------------------------
Dave Steffen, Ph.D.      
Software Engineer IV              Disobey this command!
Numerica Corporation                 - Douglas Hofstadter
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