529. The hammer and other tools which give a blow depend for their
action upon inertia. A gigantic hammer might force in a nail by the
mere weight of the head resting on the nail, but with the help of
inertia we drive the nail by blows from a small hammer. We have here
inertia aiding in the production of a mechanical power to overcome the
considerable resistance which the wood opposes to the entrance of the
nail. To drive in the nail usually requires a direct force of some
hundreds of pounds, and this we are able conveniently to produce by
suddenly checking the velocity of a small moving body.
[Illustration: FIG. 71.]
530. The theory of the hammer is illustrated by the apparatus in Fig.
71. It is a tripod, at the top of which, about 9' from the ground, is
a stout pulley C; the rope is about 15' long, and to each end of it A
and B are weights attached. These weights are at first each 14 lbs.
I raise A up to the pulley, leaving B upon the ground; I then let go
the rope, and down falls A: it first pulls the slack rope through, and
then, when A is about 3' from the ground, the rope becomes tight, B
gets a violent chuck and is lifted into the air. What has raised B? It
cannot be the mere weight of A, because that being equal to B, could
only just balance B, and is insufficient to raise it. It must have been
a force which raised B; that force must have been something more than
the weight of A, which was produced when the motion was checked. A was
not stopped completely; it only lost some of its velocity, but it could
not lose any velocity without being acted upon by a force. This force
must have been applied by the rope by which A was held back, and the
tension thus arising was sufficient to pull up B.
531. Let us remove the 14 lb. weight from B, and attach there a weight
of 28 lbs., A remaining the same as before (14 lbs.). I raise A to
the pulley; I allow it to fall. You observe that B, though double the
weight of A, is again chucked up after the rope has become tight. We
can only explain this by the supposition that the tension in the rope
exerted in checking the motion of A is at least 28 lbs.
532. Finally, let us remove the 28 lbs. from B, put on 56 lbs., and
perform the experiment again; you see that even the 56 lbs. is raised
up several inches. Here a tension in the rope has been generated
sufficient to overcome a weight four times as heavy as A. We have then,
by the help of inertia, been able to produce a mechanical power, for a
small force has overcome a greater.
533. After B is raised by the chuck to a certain height it descends
again, if heavier than A, and raises A. The height to which B is
raised is of course the same as the height through which A descends.
You noticed that the height through which 28 lbs. was raised was
considerably greater than that through which the 56 lbs. was raised.
Hence we may draw the inference, that when A was deprived of its
velocity while passing through a short space, it required to be opposed
by a greater force than when it was gradually deprived of its velocity
through a longer space. This is a most important point. Supposing I
were to put a hundredweight at B, I have little doubt, if the rope were
strong enough to bear the strain, that though A only weighs 14 lbs., B
would yet be raised a little: here A would be deprived of its motion in
a very short space, but the force required to arrest it would be very
great.
534. It is clear that matters would not be much altered if A were to be
stopped by some force, exerted from below rather than above; in fact,
we may conceive the rope omitted, and suppose A to be a hammer-head
falling upon a nail in a piece of wood. The blow would force the nail
to penetrate a small distance, and the entire velocity of A would have
to be destroyed while moving through that small distance: consequently
the force between the head of the nail and the hammer would be a very
large one. This explains the effect of a blow.
535. In the case that we have supposed, the weight merely drops
upon the nail: this is actually the principle of the hammer used in
pile-driving machines. A pile is a large piece of timber, pointed and
shod with iron at one end: this end is driven down into the ground.
Piles are required for various purposes in engineering operations. They
are often intended to support the foundations of buildings; they are
therefore driven until the resistance with which the ground opposes
their further entrance affords a guarantee that they shall be able to
bear what is required.
536. The machine for driving piles consists essentially of a heavy
mass of iron, which is raised to a height, and allowed to fall upon
the pile. The resistance to be overcome depends upon the depth and
nature of the soil: a pile may be driven two or three inches with
each blow, but the less the distance the pile enters each time, the
greater is the actual pressure with which the blow forces it downwards.
In the ordinary hammer, the power of the arm imparts velocity to the
hammer-head, in addition to that which is due to the fall; the effect
produced is merely the same as if the hammer had fallen from a greater
height.
537. Another point may be mentioned here. A nail will only enter a
piece of wood when the nail and the wood are pressed together with
sufficient force. The nail is urged by the hammer. If the wood be
lying on the ground, the reaction of the ground prevents the wood from
getting away and the nail will enter. In other cases the element of
_time_ is all-important. If the wood be massive less force will make
the nail penetrate than would suffice to move the wood quickly enough.
If the wood be thin and unsupported, less force may be required to make
it yield than to make the nail penetrate. The usual remedy is obvious.
Hold a heavy mass close at the back of the wood. The nail will then
enter because the augmented mass cannot now escape as rapidly as before.