Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

THE HAMMER.

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.

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.