Huygens clock with pendulum regulator and spindle escapement
The most significant improvements in the clock mechanism were made in the second half of the 17th century by the famous Dutch physicist Huygens, who created new regulators for both spring and weight clocks. The yoke used before for several centuries had many shortcomings. It is even difficult to call him a regulator in the proper sense of the word. After all, the regulator must be capable of independent oscillations with its own frequency. The rocker was, generally speaking, only a flywheel. Many extraneous factors influenced his work, which was reflected in the accuracy of the watch. The mechanism became much more perfect when the pendulum was used as a regulator.
For the first time, the idea to use a pendulum in the simplest instruments for measuring time came to the great Italian scientist Galileo Galilei. There is a legend that in 1583 the nineteen-year-old Galileo, while in the Pisa Cathedral, drew attention to the swinging of the chandelier. He noticed, counting the beats of the pulse, that the time of one oscillation of the chandelier remained constant, although the swing was getting smaller and smaller. Later, starting a serious study of pendulums, Galileo found that with a small swing (amplitude) of swing (only a few degrees), the period of oscillation of the pendulum depends only on its length and has a constant duration. Such oscillations became known as isochronous. It is very important that in isochronous oscillations the period of oscillation of the pendulum does not depend on its mass. Thanks to this property, the pendulum turned out to be a very convenient instrument for measuring short periods of time. Based on it, Galileo developed several simple counters that he used in his experiments. But due to the gradual damping of oscillations, the pendulum could not serve to measure long periods of time.
The creation of pendulum clocks consisted in connecting a pendulum to a device for maintaining its oscillations and counting them. At the end of his life, Galileo began to design such watches, but things did not go further than developments. The first pendulum clocks were created after the death of the great scientist by his son. However, the device of these watches was kept in strict confidence, so they did not have any influence on the development of technology. Independently of Galileo, in 1657 Huygens assembled a mechanical clock with a pendulum. When replacing the rocker arm with a pendulum, the first designers faced a difficult problem: as already mentioned, the pendulum creates isochronous oscillations only at a small amplitude, meanwhile, the spindle escapement required a large span. In the first hours of Huygens, the swing of the pendulum reached 40-50 degrees, which adversely affected the accuracy of the movement. To compensate for this shortcoming, Huygens had to show miracles of ingenuity. In the end, he created a special pendulum, which, during the swing, changed its length and oscillated along a cycloid curve. Huygens' clocks were incomparably more accurate than clocks with
rocker. Their daily error did not exceed 10 seconds (in watches with a yoke regulator, the error ranged from 15 to 60 minutes).
A remarkable example from the history of the application of physical discoveries is the history of clocks.
In 1583, nineteen-year-old student Galileo Galilei, observing the vibrations of a chandelier in a cathedral, noticed that the period of time during which one vibration occurs is almost independent of the amplitude of the vibrations. To measure time, the young Galileo used his pulse, because there were no accurate clocks then. So Galileo made his first discovery. Subsequently, he became a great scientist (we will meet his name more than once on the pages of this textbook).
This discovery of Galileo was used in the 17th century by the Dutch physicist Christian Huygens (we will learn about his discoveries in high school when we study light phenomena). Huygens designed the first pendulum clock: in them, time is measured by the number of vibrations of a weight suspended on a rod. Pendulum clocks were much more accurate than their predecessors - hourglasses, water clocks and sundials: they lagged behind or were in a hurry by only 1-2 minutes a day. And today, in some houses, you can still see pendulum clocks (Fig. 2.4, a): they are ticking measuredly, turning seconds of the future into seconds of the past.
Rice. 2.4. The first accurate clocks were pendulum clocks, but they were quite bulky (a). Spring watches are much more convenient - they can be worn on the hand (b). The most common today are quartz watches (c)
However, pendulum clocks are rather bulky: they can be placed on the floor or hung on the wall, but they cannot be put in a pocket or worn on the arm. In the 17th century, the English physicist Robert Hooke, studying the properties of springs, discovered the law that was later named after him (we will get to know this law shortly). One of the consequences of Hooke's law is similar to the discovery of the young Galileo: it turns out that the period of time during which the spring makes one oscillation is also almost independent of the amplitude of the oscillations. This allowed the construction of spring clocks (18th century). Master watchmakers learned to make them so small that they could be carried in a pocket or on a hand (fig. 2.4, b). The accuracy of a spring clock is about the same as a pendulum clock, but the spring clock must be wound every day, and besides, they sometimes begin to rush or lag, or even stop altogether. How many people were late for a train or a date just because their watch was slow or they forgot to start it that day!
In the 20th century, by studying the electrical properties of quartz (a common mineral), scientists and engineers created quartz watches - much more reliable and accurate than spring ones. Quartz watches do not need to be wound: they run on a battery that lasts for several months and even years, and the error of their course is no more than a few minutes per year. Nowadays, it is quartz watches that have become the most common (Fig. 2.4, c).
And the most accurate today are atomic clocks, the action of which is based on the vibrations of atoms.
Gravity acceleration
Galileo drew attention to the fact that any falling body first flies slowly, and then faster and faster - its movement accelerates. The scientist wanted to measure exactly how much the fall is accelerating, that is, how much the speed of a falling object increases every second. But how to make such measurements? Dropping balls from a high tower is useless: they fall too fast, and Galileo had nothing to measure short periods of time - stopwatch clocks did not exist then.
The scientist decided to slow down the fall so that it became accessible to the dimension with its meager means. Suppose, Galileo decided, the ball rolls down an inclined groove. If the slope is small, the ball will roll so slowly that you can follow the change in its speed.
Galileo took a board three fingers thick and twelve cubits long (in our measurements, this is about seven meters), put it on edge and cut a groove along the entire board. He pasted over the groove with the smoothest parchment, and carefully smoothed and polished the parchment so that the small bronze ball rolled along the groove without interference.
However, for measurements, he still needed a watch. There was some kind of clock then, but with a very imperfect mechanism. A contemporary of Galileo, the astronomer Tycho Brahe bought a mechanical clock for his observatory, but hardly used it. They were extremely capricious and unreliable.
In a word, Galileo did not have a clock. Such an obstacle, of course, could not stop him. Galileo made a homemade water clock.
He took a bucket, drilled a hole in its bottom and put a glass under it. Galileo poured water into the bucket and plugged the hole.
During the experiments, the scientist let the ball down the chute with one hand, and controlled his watch with the other: let the ball go and open the hole, and as soon as the ball reaches the intended line, he plugs the hole and removes the glass with water running into it.
Galileo weighed a glass and determined the time intervals by the amount of water collected in it. He jokingly said:
My seconds are wet, but I can weigh them.
Of course, with this method of measuring time, it was very easy to make a mistake. To reduce the magnitude of a possible error, Galileo repeated each experiment several times, trying to train himself in such a way that he could open and close a hole in a bucket of water as quickly as possible. In this troublesome business, the scientist acquired great skill.
First, Galileo launched the ball from the upper end of the inclined chute so that it rolled along its entire length. In this case, a full glass was filled with water. Then Galileo marked the groove along the length into four equal parts and began to notice the time during which the ball ran only a quarter of the entire path. At the same time, only half a cup of water was collected - exactly half as much as in the first case.
Then the scientist rolled the ball from the middle of the gutter, that is, let it run half the way, and again weighed the running water.
Galileo made several hundred such experiments and became convinced that the fall of a ball along an inclined chute is not just accelerated motion, but uniformly accelerated.
The speed of the falling ball increases evenly - it arrives every second, so to speak, in equal portions. Free falling objects follow the same law.
However, Galileo himself failed to accurately measure how much the speed of falling objects increases - he made a mistake that reduced the acceleration exactly, by half. This error of Galileo was corrected by other scientists. It has now been established that a freely falling body accelerates its motion by 9.81 meters per second in one second.
The value of 9.81 meters per second is called the acceleration due to gravity.
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But at home in his office, which became the first physical laboratory on our planet, Galileo managed to slow down the fall. It became accessible to the eye and careful, unhurried study.
For this Galileo built a long (twelve cubits) inclined chute. From the inside upholstered it with smooth skin. And he lowered polished balls of iron, bronze, and bone along it.
Did, for example.
A thread was attached to the ball, which was in the gutter. He threw it over the block, and hung a weight to its other end, which could fall or rise vertically. The weight was pulled down by its own weight, and up, through the thread, by a ball from an inclined chute. As a result, the ball and the weight moved as the experimenter wanted - up or down, quickly or slowly, depending on the slope of the chute, the weight of the ball and the weight of the weight. The ball and weight could thus move under the influence of gravity. And that was the fall. True, not free, artificially slowed down.
First, Galileo found the law of the steady state of this system: the weight of the weight, multiplied by the height of the raised end of the inclined chute, must be equal to the weight of the ball, multiplied by the length of the chute. This is how the equilibrium condition for the system appeared - the Galilean law of the inclined plane.
Nothing has yet been said about the fall and its secrets.
Immobility is not difficult to study: it is constant in time. Seconds, minutes, hours go by, nothing changes.
Scales and rulers - that's all you need for measurements *.
* (That is why, from ancient times, statics began to develop - a field of physics that deals with all kinds of immobility: balanced weights, blocks, levers. All these things are necessary, it is important and useful to understand them, it is not for nothing that the famous Greek Archimedes devoted a lot of time to them. Even in immobility, he noticed much that the inventors of "possible machines" need. However, to be picky, this was not yet real physics. It was only a preparation for it. Genuine physics began with the study of motions.)
Then Galileo began to study the movement of balls. This very day was the birthday of physics (alas, its calendar date is unknown). Because it was then that the time-varying process was subjected to the first laboratory study. Not only rulers were used, but also watches. Galileo learned to measure the duration of events, that is, to perform the main operation inherent in any physical experiment.
The legend about Galileo's laboratory clock is instructive. At that time it was impossible to buy a stopwatch in the store. They haven't even invented walkers yet. Galileo, on the other hand, got out of the situation in a very special way. He counted the time with the beats of his pulse, then, as old biographers assure, he made a good laboratory clock from unexpected components: a bucket, scales and a crystal glass. In the bottom of the bucket he made a hole through which an even stream of water flowed. From the sun, I noticed how many ounces of water flowed out in an hour, and then calculated the weight of the water flowing out in a minute and a second.
And here is the experience. The scientist lowers the ball into the chute and immediately substitutes a glass under the stream. When the ball reaches a predetermined point, it quickly pushes the glass away. The longer the ball rolled, the more water flowed. It remains to be put on the scales - and the time is measured. Why not a stopwatch!
"My seconds are wet," said Galileo, "but they can be weighed."
Observing elementary rigor, it is worth noting, however, that this watch is not as simple as it might seem. It is unlikely that Galileo took into account the decrease in pressure (and hence the speed) of the water jet with a decrease in the level of water in the bucket. This can be neglected only if the bucket is very wide and the stream is narrow. Perhaps that is how it was.
The problem of measuring time has long been faced by man. Today's human society could not possibly exist at all without clocks - instruments for accurate measurement of time. Trains wouldn't be able to run on time, factory workers wouldn't know when to come to work and when to go home. Schoolchildren and students faced the same problem.
In principle, a person learned to measure sufficiently large periods of time a long time ago, even at the dawn of his development. Such concepts as "day", "month", "year" appeared even then. The first to divide the day into periods of time were probably the ancient Egyptians. There were 40 nut in their day. And if a period of time in one day can be measured in a natural way (this is the time between two climaxes of the Sun), then special instruments are needed to measure shorter periods of time. These are sun, hour and water clocks. (Although, you can’t determine the moment of the Sun’s climax without special devices either. The simplest special device is a stick stuck in the ground. But more on that some other time.) All these types of watches were invented back in ancient times and have a number of drawbacks : they are either too inaccurate or measure too short periods of time (for example, an hourglass, more suitable as a timer).
Of particular importance was the accurate measurement of time in the Middle Ages, in the era of the rapid development of navigation. Knowing the exact time was necessary for the ship's navigator to determine geographic longitude. Therefore, a particularly accurate instrument for measuring time was required. For the operation of such a device, a certain standard is needed, an oscillatory system that oscillates in strictly equal time intervals. The pendulum became such an oscillatory system.
A pendulum is a system suspended in a gravitational field and performing mechanical oscillations. The simplest pendulum is a ball suspended from a string. The pendulum has a number of interesting properties. The most important of them is that the period of oscillation of the pendulum depends only on the length of the suspension and does not depend on the mass of the load and the amplitude of the oscillations (that is, the magnitude of the swing). This property of the pendulum was first investigated by Galileo.
Galileo Galilei
Galileo was prompted to deep research on pendulums by observing the vibrations of a chandelier in the Pisa Cathedral. This chandelier hung from the ceiling on a 49-meter suspension.
Pisa Cathedral. In the center of the picture is the same chandelier.
Since there were no precise instruments for measuring time then, in his experiments Galileo used the beating of his heart as a standard. He published a study of the oscillations of a pendulum and stated that the period of oscillations does not depend on their amplitude. It was also found that the periods of oscillation of pendulums are related as the square roots of its length. These studies interested Christian Huygens, who was the first to propose the use of a pendulum as a standard for regulating the movement of clocks and the first to create a really working sample of such clocks. Tried to create a pendulum clock and Galileo himself, but he died before he could finish this work.
One way or another, but for several centuries ahead, the pendulum became the standard for regulating the clock. The pendulum clocks created during this period had high enough accuracy to be used in navigation and in scientific research and just in everyday life. Only in the middle of the twentieth century, he gave way to a quartz oscillator, used almost everywhere, since the frequency of its oscillations is more stable. For even more accurate time measurement, atomic clocks with an even more stable oscillation frequency of the regulator are used. They use a cesium time standard for this.
Christian Huygens
Mathematically, the law of pendulum oscillation is as follows:
In this formula: L- suspension length, g- acceleration of gravity, T- the period of oscillation of the pendulum. As we can see, the period T does not depend on the mass of the load, nor on the amplitude of oscillations. It depends only on the length of the suspension, and also on the value of the free fall acceleration. That is, for example, on the Moon, the period of oscillation of the pendulum will be different.
And now, as I promised, I give the answer to the problem published. In order to measure the volume of a room, you need to measure its length, width and height, and then multiply them. This means that some standard of length is needed. Which? We don't have a line! We take the shoe by the lace and swing it like a pendulum. With a stopwatch, we measure the time of several oscillations, for example, ten, and dividing it by the number of oscillations, we get the time for one oscillation, that is, the period T. And, if the period of oscillation of the pendulum is known, then from the formula already known to you it doesn’t cost anything to calculate the length of the suspension, that is, the lace. Knowing the length of the lace, using it as a ruler, we can easily calculate the length, width and height of the room. Here is a solution to a seemingly difficult problem!
Thank you for your attention!!!