Re: Weight and Mass

[Bernard Cleyet <anngeorg@PACBELL.NET>]

the cw torque due to a slightly larger mass on the right pan (of an equal arm
balance) is delta(m)* g* cos (a) * r.       r if the length of the arm(s)

the ccw (restoring) torque is M*g* L *sin (a).    L is the position of the
centre of mass (M) of the balance below the bearing (pivot).   I've assumed
the arms have no mass.  I don't think that makes a diff.

Anyway if g is uniform down they (g's) cancel,  so the sensitivity:   delta m
= sin (a)* M*L / (cos(a)* r)   which looks correct intuitively, except for the
trig. (I'm not that good.)  Obviously if in balance a is zero. Therefore,
delta m is zero.    OK

bc



"John S. Denker" wrote:

> At 04:58 PM 9/27/01 -0500, brian whatcott conjectured:
> > ... that though beam balances measure mass:
> > the pointer reading is still g dependent, like a spring scale.
>
> Does anybody have any experimental and/or theoretical support for this
> conjecture?
>
> There seems to be overwhelming theoretical evidence to the contrary.
>
> One form of the theoretical argument appeals to linearity and
> superposition, as follows:
>
> There will be some part of the beam-balance that represents "down".  This
> will be determined by the center of mass relative to the position of the
> pivot.  The calculation of center of mass is independent of g.  If we
> increase the magnitude of g, down is still down, only more so.  The
> configuration of the pointer should be unaffected.  This assumes of course
> an ideal non-deforming springless beam-balance.
>
> There are probably other arguments that lead to the same conclusion.
>
> There is also some suggestive experimental evidence: Highly-accurate
> laboratory balances have no provision for calibration, except in the Nth
> decimal place, whereas we know that g varies significantly from location to
> location.