Apparatus for the study of central forces

50 x 19 x 73
Carved inlayed wood and brass

INDEX 1788 : H.V.198

Duae regulae ligneae, quarum utrique insident duae parastatae, quae superius conjunguntur arcu, qui trochleam sustinet, cum filis metallicis, per quae excurrunt binae situlae ex orichalco. Varia pondera plumbea cylindrica.

Two wooden rulers on which two columns are placed and are united on top by a hoop which supports a pulley with metallic strings, through which two brass buckets run. Various cylindrical lead weights.

With this device, it is possible to study the characteristics of the central force that should act on a body so that it can describe a circular movement. It consists of a horizontal wooden board, to which 2 wooden columns are fixed perpendicularly. These columns are located in the middle of the board, together forming the shape of an inverted T.

Two hollow brass cylinders with a lid on the top of each one, are joined together by a flexible but inextensible string. One of the cylinders moves vertically between the two columns, while the other sits on a small brass platform. This one may move along the horizontal board by means of two brass rods mounted on the board. There is a pulley on the top part of the columns and another near the vertex of the assemblage formed by the base and the two columns. The string that joins the cylinders passes through these pulleys.

On the base board, there are two holes, allowing this system to be adapted to a rotation machine. This machine would act upon the apparatus, making it rotate around a vertical axle which passes through the middle of that base. The speed of the rotation of the apparatus could be controlled by the person working the machine.

When the apparatus is not in movement, the cylinders should be positioned so that the cylinder which moves between the two vertical columns is at the base of these. The other cylinder should be near the intersection of the columns and the board, that is, about the middle of the base.

When the apparatus was put into rotation the cylinder which is located between the two columns used to make a rotating movement linked to that of the axle of rotation of the apparatus. The other cylinder used to make a circular trajectory around this axle. So that it remains in this state of motion, the string to which it is attached had to exert a centripetal force upon it of an intensity F = m w2 r, m being the mass of the cylinder, r the radius of its trajectory and w the angular speed of the whole.

As the speed of rotation increased, it was also necessary to increase the tension on the string. When a certain amount of angular speed was reached, the tension on the string would become greater than the weight of the cylinder suspended between the columns and, as a result, it would rise with an accelerated motion, causing the second cylinder to move towards the periphery. In order to maintain a new circular trajectory this cylinder would need renewed tension on the string, which would then cause an increase in the acceleration of the first cylinder, and, in turn, cause the second to move towards the periphery. It can be observed that once the initial situation of dynamic equilibrium is destroyed, it is impossible to recover it, even if the speed of rotation of the apparatus does not increase. Unless, of course, one of the cylinders should run into an obstacle, which would prevent either the ascension of the cylinder between the columns or the movements to the periphery of the cylinder above the board, or unless the angular velocity were to be decreased.

The fact that the cylinders are hollow, and have a lid on the top which can be closed, made it possible to place small objects in the interior of each and any of them, changing their masses for different experiments. In this way, it was possible to evaluate the influence of the mass of the cylinders on the behaviour of the system. The dynamic equilibrium has to be maintained for a higher angular speed when the mass of the cylinder which makes the circular trajectory is decreased. The same happens when the mass of the cylinder suspended between the columns is increased.

The horizontal platform has a series of small wedges, oriented in a way which allows the radius of the curvature of the circular trajectory made by the cylinder to have different values at the beginning of the experiment. The further away from the columns it is placed, the more force would be needed to keep it at a given circular trajectory. As a consequence, the deviation from the dynamic equilibrium would occur for lower angular speed.

The rotation machine which was intended for various experiments involving circular motion no longer exists. According to the Index Instrumentorum, the model of this machine that was in the Gabinete de Física in Coimbra corresponded to that which ´s Gravesande presents in his book, Physices Elementa. It must have been, most certainly, one of the most remarkable machines in the collection. It was made of the most excellent Brazilian wood with various metal and brass pieces.

From Colégio dos Nobres, catalogue n.º 188.

Nollet, Jean Antoine, Leçons de Physique Expérimentale, Paris, 1764, Tomo II, Leçon V, P1. 4, Fig. 20-21.
's Gravesande, Willem Jacob, Physices Elementa, Leiden, 1742, § 567, Tab. XX and Tab. XXI, fig. 1,2,3, I and II, p. 193.

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