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A DOUBLE CONE WITH RUNNER

Number in the past inventory 2883                                                                                               Number in the current inventory 72

INSTRUMENT: A DOUBLE CONE WITH RUNNER

Age: beginning of the twentieth century

Creator: /

Materials: Brass, wood

Size: (22.6 x 18.6 x 10.5) mm

State of conservation: Good

Information: From the information contained in the old inventory register, found in the school, the instrument is said to have been added to the inventory with the number 2883 on 26th June 1928 priced at 450 liras.

Description: The instrument consists of a triangular runner (an inclined plane with diverging sides) the sides of which are of the same length; they form two brass tracks supported at the top by a wooden leg (3.2); the base of the triangle consists of a shaped wooden rod (6,1) that holds the bars allowing the sliding of a double cone (Ø8 x 19). Each apex of the wooden double cone has a little rod that allows the housing of the instrument in a rest position in the two grooves that are located at the upper end of the bars.

Use: This instrument is used to determine the force required to balance the weight force as the inclination of the plane varies.

Learn more

Between the eighteenth and nineteenth centuries, physicists from research laboratories got involved in the building of instruments that would astonish and instruct at the same time, demonstrating the laws of physics even though in the eyes of the observer the instrument seemed to break them (mechanical paradox). Among these the most well known is the double cone.

This instrument consists of two divergent and uphill tracks supporting two cones adhered at the bases. The double cone placed at the top of the slide starts to roll spontaneously (moved by gravity only, without any push), going up the tracks that support it and at the end of its movement it arrives at the top of the uphill (as you can see in the picture).

But how can we explain this phenomenon? This instrument behaves abnormally only apparently: experience teaches us that any body placed at the top of any slide falls down. This is because the center of gravity of every body is inevitably drawn towards the center of the earth, as the law of motion of the center of gravity says (“The motion of a continuous system of material points subjected to external forces is determined only by the motion of its center of gravity, including the entire mass of the system and is subjected to the resultant of the external forces”). And the double cone is not an exception! In fact the law does not refer to all the points constituting the body but it concerns only its center of gravity; therefore only the center of gravity must be observed. In fact, although apparently the totality of the points of the body goes uphill, the center of the mass goes down, consistently with the theorem described above, since the tracks diverge more and more while it is going up.

This can be schematized as a continuous system of material points, therefore the body is moved only by gravity, with negligible frictional forces.

The eye instinctively notices the “general” motion of the body focusing on the tracks and in particular on their inclination regarding the rolling of the body along them, while we must consider only the motion of the center of gravity of the solid.

As a conclusion: a paradox? Yes, it is, but absolutely logical!

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