Galileo’s Experiments on Accelerated Motion

A short account of Galileo’s description of his own experiment on accelerated motion — a short account of it, the apparatus he used and the results he got.

The first argument that Salviati proves is that in accelerated motion the change in velocity is in proportion to the time (𝑣 ∝ 𝑡) since the motion began, and not in proportion to the distance covered (𝑣 ∝ 𝑠) as is believed by Sargedo.

“But for one and the same body to fall eight feet and four feet in the same time is possible only in the case of instantaneous (discontinuous) motion; but observation shows us that the motion of a falling body occupies time, and less of it in covering a distance of four feet than of eight feet; therefore it is not true that its velocity increases in proportion to the space. (Salviati)

Also, he proves that the increase in proportion is not of simple doubling but larger. They agree upon a definition of uniformly accelerated motion,

“A motion is said to be equally or uniformly accelerated when, starting from rest, its momentum receives equal increments in equal times. (Sargedo)

To this definition Salviati adds an assumption about inclined planes, this assumption is that for a given body, the increase in speed while moving down the planes of difference inclinations is equal to the height of the plane. This also includes the case if the body is dropped vertically down, it will still gain the same speed at end of the fall as it would gain from rolling on the incline This assumption makes the final speed independent on the profile of the incline. For example, in the figure below, the body falling along𝐶 → 𝐵, 𝐶 → 𝐷 and 𝐶 → 𝐴 will attain the same final speed.

This result is also proved via a thought experiment (though it might be feasible to do this experiment) for a pendulum. The pendulum rises to the height it was released from and not more.

After stating this theorem, Galileo then suggests the experimental verification of the theorem. of The actual apparatus that Galileo uses is an wooden inclined slope of following dimensions: length 12 cubits (≈ 5.5 m, 1 cubit ≈ 45.7 cm), width half-cubit and three-finger breadths thick . In this plank of wood, he creates a very smooth groove which is about a finger thick. (What was the thickness of Galileo’s fingers?) The incline of this plank are changed by lifting one end. A bronze ball is rolled in this groove and time taken for descent is noted.

“We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one- tenth of a pulse-beat.

Then Galileo performed variations in the experiment by letting the ball go different lengths (not full) of the incline and “found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane”. Each variation was repeated hundreds of times so as to rule out any errors. Also, the fact that for different inclines the times of descent were in noted and were in agreement with the predictions.

Since there were no second resolution clocks to measure time, Galileo devised a method to measure time using water. This was not new, water clocks were used earlier also.

The basic idea was to the measure the amount of water that was collected from the start of the motion to its end. The water thus collected was weighed on a good balance.This weight of water was used as a measure of the time. A sort of calibration without actually measuring the quantity itself: “the differences and ratios of these weights gave us the differences and ratios of the times”

Galileo used a long incline, so that he could measure the time of descent with device he had. If a shorted incline was used, it would have been difficult to measure the shorter interval of time with the resolution he had. Measuring the free fall directly was next to impossible with the technology he had. Thus the extrapolation to the free fall was made continuing the pattern that was observed for the “diluted” gravity.

“You present these recondite matters with too much evidence and ease; this great facility makes them less appreciated than they would be had they been presented in a more abstruse manner. For, in my opinion, people esteem more lightly that knowledge which they acquire with so little labor than that acquired through long and obscure discussion. (Sargedo)

 

Reference

Dialogues Concerning Two New Sciences

Book Review: Ages in Chaos by Stephen Baxter

Ages in Chaos is a scientific biography of James Hutton by Stephen Baxter. Hutton was a Scottish scientist who also played his part in Scottish enlightenment. Hutton was the first to speculate on the idea deep time required for geological processes at the end of 1700s arguing with evidence he collected. He was trained as a medical doctor, practiced farming for 10 odd years and had continued his explorations of geology throughout. The prevalent theories of geology, called Neptunists, posited that water was the change agent. Hutton on the other hand posited that it was heat which was responsible for changes, hence Vulcanists. Also, another thing was that of time needed for this change. As others of his era, Hutton was deeply religious, like Newton, wanted to find evidence for creation as per bible.

During his time, especially popular was the idea of flood as per Bible, while the Earth was literally considered to be 6000 years old. This created a problem for Hutton, who was labelled to be atheist and heretic for suggesting that Earth is much older and that there was no design. But Hutton was a conformist and wanted to find a uniform evidence for all observable aspects. He was not like a modern scientist, as he is painted many times. The ideas were vehemently attacked on each point. Though he went to the field to find geological examples for this theory. James Watt, Black and John Playfair were his friends and provided him with evidence in the form of rock samples. During his lifetime, Hutton’s ideas will not find much audience. But due to his friends, his ideas sustained a a barrage of criticisms. Only in the next generation with Lyell this work would find acceptance. This idea of a deep time was crucial in formation Darwin’s theory.

https://www.goodreads.com/book/show/157978.Ages_in_Chaos

The book reads well mostly, but at times a complete lack of illustrations in the forms of geological artefacats and maps (of Scotland) makes it difficult to read well.

Book Review: Pendulum: Léon Foucault and the Triumph of Science by Amir D. Aczel

The book traces Leon Foucault’s ingenious approach to solving the problem of providing a terrestrial proof of rotation of the Earth. The pendulum he devised oscillates in a constant plane, and if properly engineered (as he did) can actually show the rotation of the Earth. The demonstration is one the most visually impressive scientific experiments. Also, Foucault gave prediction, an equation which would tell us how the pendulum will behave at different parts of the Earth. The pure mathematicians and physicists alike were taken aback at this simple yet powerful demonstration of the proof which eluded some of the most brilliant minds, which includes likes of Galileo and Newton. Rushed mathematical proofs were generated, some of the mathematicians earlier had claimed that no such movement was possible. That being said, Foucault was seen as an outsider by the elite French Academy due to his lack of training and degree. Yet he was good in designign things and making connections to science. This was presented to the public in 1851, and the very next year in 1852 he created another proof for rotation of the Earth. This was done by him inventing the gyroscope.. Gyroscope now plays immense role in navigation and other technologies. Yet he was denied membership to the Academy, only due to interest of the Emperor Napolean III in his work in 1864. The pendulum is his most famous work, but other works are also of fundamental significance.

  • He was first person to do photomicrography using Daguerreotype
  • Accurate measurment of speed of light using rotating mirrors –
  • Devised carbon arc electric lamp for lighting of micrcoscope
  • One of the first to Daguerreotype the Sun
  • Designed the tracking systems used in telescopes
  • also designed many motors, regulators to control electrical devices

There are a couple of places in the book where Aczel seems to be confused, at one point he states parallax as a proof for rotation of Earth around its axis, whearas it is more of a proof of Earths motion around the Sun. At another place he states that steel was invented in 1800s which perhaps he means to say that it was introduced in the west at the time. Apart from this the parallels between the rise of Napoleon III, a Nephew of Napolean, to form the second Empire in France and Foucault’s own struggle for recognition of his work and worth is brought out nicely.

Thomas Kuhn on the role of textbooks in science education

The single most striking feature of this [science] education is that, to an extent wholly unknown in other fields, it is conducted entirely through textbooks. Typically, undergraduate and graduate students of chemistry, physics, astronomy, geology, or biology acquire the substance of their fields from books written especially for students.

Thomas Kuhn The Essential Tension

Here Kuhn is trying to show us the nature of science education which is usually divergent from the historical processes and events which led to the currently accepted theories. Most of the textbooks rather show the content matter which makes sense conceptually in a rationally organised manner. Of course, the ideal goal, at least in the physical sciences, is to create a hypothetico-deductive model in which a given theory, its predictions, explanations and implications can be derived from some basic definitions and axioms. For example, an introductory text on motion in physics usually starts with definitions and assumptions usually of a mass point, and/or operations that are defined on it. The text does not describe the historical conditions in which this conceptual approach arose, rather it adapts a very pragmatic pedagogical approach. It defines the term and ends it there, but in this process, it redefines the conceptual history. This approach assumes that there is no pedagogical merit or role in introducing a concept in its historical context. This perhaps is also linked to Poppers distinction of the context of discovery and the context of justification. What we see is a rational reconstruction of historical processes to make sense of them in a straightforward manner.

 

 

Science, a humanistic approach

Science is an adventure of the whole human race to learn to live in and perhaps to love the universe in which they are. To be a part of it is to understand, to understand oneself, to begin to feel that there is a capacity within man far beyond what he felt he had, of an infinite extension of human possibilities . . .
I propose that science be taught at whatever level, from the lowest to the highest, in the humanistic way. It should be taught with a certain historical understanding , with a certain philosophical understanding , with a social understanding and a human understanding in the sense of the biography, the nature of the people who made this construction, the triumphs, the trials, the tribulations.

I. I. RABI
Nobel Laureate in Physics

via Project Physics Course, Unit 4 Light and Electromagnetism Preface

Do see the Project Physics Course which has come in Public Domain hosted at the Internet Archive, thanks to F.  James Rutherford.