It might, perhaps, be thought, that since the weights suspended at the
ends of the thread are in equilibrium, and therefore have no tendency
either to move or to resist motion, the additional weight placed upon
one of them ought to descend as rapidly as it would if it were allowed
to fall freely and unconnected with them. It is very true that this
weight will receive from the attraction of the earth the same force
when placed upon one of the suspended weights, as it would if it were
disengaged from them; but in the consequences which ensue, there is
this difference. If it were unconnected with the suspended weights,
the whole force impressed upon it would be expended in accelerating
its descent; but being connected with the equal weights which sustain
each other in equilibrium, by the silken cord passing over the wheel,
the force which is impressed upon the added weight is expended, not
as before, in giving velocity to the added weight alone, but to it
together with the two equal weights appended to the string, one of
which descends with the added weight, and the other rises on the
opposite side of the wheel. Hence, setting aside any effect which the
wheel itself produces, the velocity of the descent must be lessened
just in proportion as the mass among which the impressed force is to
be distributed is increased; and therefore the _rate_ of the fall
bears to that of a body falling freely the same proportion as the added
weight bears to the sum of the masses of the equal suspended weights
and the added weight. Thus the smaller the added weight is, and the
greater the equal suspended weights are, the slower will the rate of
descent be.
To render the circumstances of the fall conveniently observable, a
vertical shaft (see _fig. 24._) is usually provided, which is
placed behind the descending weight. This pillar is divided to inches
and halves, and of course may be still more minutely graduated, if
necessary. A stage to receive the falling weight is moveable on this
pillar, and capable of being fixed in any proposed position by an
adjusting screw. A pendulum vibrating seconds, the beat of which ought
to be very audible, is placed near the observer. The loaded weight
being thus allowed to descend for any proposed time, or from any
required height, all the circumstances of the descent may be accurately
observed, and the several laws already explained in this chapter may be
experimentally verified.
Public-domain text, read in full here on John Shaqi.
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