Simple Tools

July 17, 2014

Mechanical Tools

In the modern world, there are always new products, new features, and new designs. In the midst of this, it is crucial to not take for granted the tools which have carried humanity through thousands of years. This is crucial because ignorance of the true value and origin of such tools will lead to an overwhelming dependence on high-level technologies that are serviced "by someone else", and a completely helpless state when such technologies fail. These tools are in fact of such importance and so ideally suited to their purpose that all modern technology and manufacturing methods has essentially changed nothing about them and they could be exchanged with those used hundreds of years ago without difficulty.

In this article, tools that can be considered mechanical in nature are considered specifically. Despite this focus the reader is reminded to not dismiss tools that fit the above 'timeless' criterion, such as kitchen utensils (pots, pans, knives), fire and heat tools, shoes and clothes, jars and containers, brooms, etc.

By a mechanical nature, it is meant that the tool is designed specifically to exert a force on a single object in order to move it. Two broad categories of these tools are the hammer (impact tools) and the crowbar (lever tools).

The hammer (impact)

The hammer is a very interesting tool from a physics perspective. Why does it work? Perhaps that is too fundamental, we should first ask How does it work? Indeed it is seen that, through no fancy gears or ratchets, the energy that our hands can exert with the use of a hammer can be transferred to a nail, a board, or any other object, with much less effort and pain than if a similar act were attempted without the use of a hammer. How it works should be the first thing to determine.

In the act of striking a nail, a hammer begins its swing and is accelerated downwards both by the hand of the user and by gravity. It attains a certain velocity, which along with its mass can be used to provide a measure of kinetic energy. The highest value of the energy obtained is immediately before the hammer hits the nail, as at that point it has experienced acceleration for the longest time it is allowed. When the hammer hits the nail, all of its energy must go somewhere (conservation of momentum gives a general idea of where). At this point an interesting set of events occurs.

The entire nail is compressed as the hammer begins to transfer its energy. The nail acts like a very stiff spring, exerting an equal force on both the hammer and the surface into which its point is being driven. The force that it is able to exert is however based on the material into which it is being driven, and in fact equal to the 'resistance' that the material provides. Now since the energy in the hammer is dependent only on how it was accelerated and not on any properties of the nail or nailed material, and energy is the product (integral) of force and distance, it can be seen that if the nail can provide different resistive forces to the hammer it must also provide different resistance distances. Namely, with a similar hammer swing, a nail being driven into a soft material like clay will provide only a small force to slow down the hammer, and it will be driven a long way, while a nail being driven into hardwood will provide a larger force and be driven in by only a small amount. It can also be shown that in both cases the time that the hammer takes to drive the nail is proportional to the distance by which the nail is driven. If the nail be driven into an extremely stiff material, the force exerted by the hammer will be large and the distance the nail moves will be small - so small that the nail will compress to absorb the hammer's energy and then attempt to return this energy to the hammer - without moving into the material even a little bit. Thus it tends to be that nailing soft wood is easier on the arm than nailing hardwood, since in the latter case more energy is returned to the hammer by the nail (acting as a spring) and this energy must be removed by the arm muscles. Like a simple experiment with an ordinary metallic spring easily shows, a spring that is compressed and unsupported will tend to buckle to one side in an attempt to expand, and a similar bending is observed when nailing into a hard surface.

Thus it is made clear that the hammer's physical response is very much dictated by the stiffness of the material into which the nail is driven, and this by dynamically varying force, distance, and time that characterize the contact between the hammer and the nail. Any of the three variables can describe the hammer's action mathematically, but physically the most intriguing one is the time difference. In this interpretation, a hammer provides a way of interaction between two different time scales - one of the order of seconds (the swing, readily accessible to man) and the other on the order of microseconds (the hit, to which man is largely ignorant except for the after-effect). This interaction takes place by using kinetic energy as a 'buffer' that is equally accessible to both timescales. Since all materials exist in time, any material could be potentially used as a hammer, although with varying effectiveness.

The distance variable is interesting on its own terms, since it provides an analogy of the hammer in terms of the lever. The lever is a device which uses the mathematical notion of 'moment' to amplify force at expense of distance. The hammer was previously said to maintain constant the force-distance product, meaning if a force amplification is achieved, a corresponding distance de-amplification will be seen. The primary difference between the two devices is that the force amplification gained by the hammer is not pre-determined but is based on the material which the nail is in. Neither is the hammer's driving distance or time determined before the nail makes contact with the hammer head. The hammer is in effect a variable-length lever, with the varying length determined solely by the stiffness of the material which it is hitting. Thus it will act as a very long lever when striking a stiff surface and as a rather short lever when striking a soft surface. Since generally force amplification rather than de-amplification is desired, a hammer is most useful for striking hard objects. For soft objects, our hands will provide sufficient force. Thus a hammer would not be used for fluffing a pillow, just as the hand would not be used for hitting a nail. Similarly, a hard hammer is a must, otherwise the material will cause the nail to be driven into the hammer - for this reason hammers are made of a harder steel than nails, and not of soft material like wood or plastic.

The dynamic nature of the hammer can be used to determine the properties of the material which the hammer is hitting (directly or indirectly). If after the hammer hit it is observed that the hammer travels a long distance downwards, the material is soft, while otherwise it is hard. This is a direct measure of how much force the material is capable of exerting. While the sound made by the material after it is struck is dependent on many properties, it is generally also indicative of material hardness. The stiffer the material is, the more energy will go into compression of the nail (or material surface) rather than its progression through the material, and this energy will be returned to both the hammer head and the material and will result in sound waves. Thus hammering into soft material can be done without much sound but hammering into hard materials will produce noise. Trying to hammer or hit very hard materials will cause a lot of energy to be dissipated as sound, which can be observed with any metal-metal hits as compared to metal-wood or wood-wood hits.

The crowbar (lever)

The crowbar is an important tool as it provides force amplification similar to the hammer, in the sense that whenever a greater force is applied it is done through a smaller distance in order to conserve energy. The important difference is that here the time parameter is fixed and equal between the applying and applied force. Any energy applied is transferred immediately, without using kinetic energy as a buffer. This means the force depends only on the distance that the object is made to travel, and this distance is determined by man. Thus by pulling on the long end of a crowbar and forcing some object on the short end to move, one is moving that object through a shorter distance than one is moving his hands, and therefore a force amplification of a controlled and constant magnitude is achieved. The longer a crowbar's handle is relative to its working end, the more force amplification can be gained, and for a particular crowbar this remains a fixed number in all usage circumstances. The inverse effect of force de-amplification and distance increase is not as widespread in tools, but some examples are rowing oars, door closers, and trebuchets (note that scissors are in fact a variable-force device).

The crowbar is seen to lack the dynamic nature of the hammer, which makes it useful for dealing with forces that require time scales accessible to humans. This includes lifting heavy objects, and holding apart a pried opening. Other uses of a crowbar, such as tearing off a lock, do not require accessible timescales, and thus might be accomplished similarly by using a hammer. A lock with a soft rubber coating however will yield to a crowbar more easily than to a hammer. Since the magnitude of force amplification is fixed, unlike in a hammer, a crowbar may be used to move even light or fragile objects by a controlled amount, in fact providing finer adjustment capacity than hands alone. Further, a crowbar by itself will not create disturbances on the sound frequency timescale, so it can be used with minimal noise regardless of the weight or stiffness of an object.