The Locomotive - Lighthouse Survival Blog

34 THE LOCOMOTIVE, [March,
pressure of the fulcrum against the lever. (It is plain that although the lever presses
7/jrwanl against the pin, the pin presses dowmcnrd against the lever.) Now since the
lever does not tip either v;ay, but remains in equilibrium, it must be that the tipping
effect of the weights is just balanced by the opposite tipping effect of the downward
pressure of P against the lever. Now the tipping effect, or moment, of any force is
proportional to the magnitude of the force, and also to the leverage it has. Thus to
find the tendency of the weight A to turn the lever about the point Fas a center, we
multiply 124 by 46;^ (46^ being the distance of this weight from V), which gives 5,735.
This means that the weight A exerts precisely the same tipping effect that a weight of
5, 735 pounds would exert, if hung on the lever at a distance of one inch from V. The
distances of B and C from V being 37| in. and 30:^ in., respectively, we find that
their respective tipping effects are 37^ x 45 and 30^ x 45, or 1,076^ and 1,361^; so that
A'^m
« •// >
C U
Figs. 3 and 4.—Details op the Casting.
the combined effect of the three weights is the same as the effect of a weight of
5,735 + 1,676| + l,361j = 8,773|^ lbs. hung on the lever at a distance of one inch from
V. To this we may add the tipping effect of the lever's own weight, which we
calculate in precisely the same manner, except that we first assume that it acts as
though its weight were concentrated at its center. The center of the lever, being 25
inches from P, is 22| inches from F, so that its tipping effect is 22^ X 17 = 3785^.
Adding this to 8,772|^ we obtain 9, 150|, which is the weight we must hang on the lever,
one inch from F, to get the same tipping tendency that we get from the actual arrangement
of things as shown in Fig. 1. Now since this tendency must be precisely equal to
the tendency of the pin P to tip the lever in the opposite direction, in order to find the
downward pressure of P we have merely to answer the question, what weight
must be hung on the lever, 2| inches from F, to get the same tipping tendency that a
weight of 9,150| lbs. gives when hung at a distance of one inch from F? And to
answer this question we have merely to divide 9,150| by 2|, which gives 3, 328 lbs.
(omitting fractions). Hence we conclude that in the arrangement shown in Fig. 1
there is a shearing strain of 3, 328 lbs. on the pin P, and therefore also a tensile strain of
3,328 lbs. on the casting which sujoport this pin.
We have next to examine the fulcrum pin P, to see if it is strong enough to withstand
this strain. This pin, which is shown best in Fig. 3, was threaded, being, in fact,
a heavy machine screw with a round head. Its diameter at the base of the thread was
.40 inch, so thatits effective sectional area was .40 x .40 x .7854 = .1357 sq. in. It will
be observed that the pin must be double-sheared, if it fails ; and hence if we allow
70,300 lbs. per square inch of single section as the strength of iron exposed to double
shear, the ultimate strength of the pin is found to be .1257 x 70,300 = 8,837 lbs. With