Article status: Draft
Time Estimate for Reading: 30 min
Learning Objectives: Introduction to displacement, velocity and acceleration
Effort Required: Medium
Pedagogy Model: Evolution
Prior Physics Concepts: Nil
Prior Math Tools: Secondary school level Arithmetic, geometry and algebra
The simple pendulum is one of the simplest and most important discoveries (1602) in science. It is simple for its construction; just a mass and a string.
For such a simple device, it is fascinating to see the wide range of applications it has been put to use:
- Gravimeter (1620)
- Clock (1656)
- Measure density of earth (1737)
- Standard for length (1791)
- Proof that earth is spinning: Foucault's pendulum (1851)
- Horizontal Pendulum: Seismograph (1880)
Even more important is the process of discovery having a rich history and spans almost 2000 years; Starting from Aristotle (350 BC) to 1602 (the Galilean era)
As the famous story goes, Galileo happens to visit a cathedral in pisa (1588), observes a swinging chandelier and discovers a pendulum. Interestingly, 14 years seems to have passed between observation of swinging mass and discovering the pendulum.
Now fast forward to the Galilean Period. 1580's.
Out of the million problems on hand (there are problems every where and every one has some problem or the other to worry about. It is only human to keep worrying), Galileo finds Aristotelian views to be interesting problems to worry upon. The view on what is matter made of?, Is earth at the center of everything? (may be because humans are the most important creatures in the universe!) and Whether bodies of different masses fall at the different rates (referred to as law of falling bodies)?
Given these three problems, the question is which one to prioritize and worry about?
1. The planets are too far away and only device known is human eye
2. On a similar and contrary note, to understand what is matter made off, we enter the regime of things that are too small for the human eye
3. The law of falling bodies "seem" to be the simplest of the three to work on and we choose to begin with this.
Having chosen the problem, we wish to know who else were interested in similar problems and find that, starting from Archimedes (250 BC), Da Vinci (1470) have observed that the bodies of different masses fall the same rate (contrary to Aristotelian beliefs)
A further analysis shows that
- In 1576, Giuseppe Moletti, Galileo's predecessor in the chair of mathematics at the university of Padua, reported that bodies of the same material but different weight, as well as bodies of the same volume but different material, dropped from a height arrived at the Earth at the same time.
- In 1586 (3 years before Galileo), Simon Stevin reported that different weights fell a given distance in the same time. His experiments, with the help of his friend Jan Cornetts de Groot, were conducted using two lead balls, one being ten times the weight of the other, which he dropped thirty feet from the church tower in Delft. from the sound of the impacts they concluded that the spheres fell with the same speed, not as stated by Aristotle. Stevin is regarded by many as the first one to perform falling bodies experiments.
A slope of 5 degrees seem to provide maximum travel time and the formula is arrived at connecting position and time; for the first time. distance traveled is proportional to the square of the time of fall.
Here again we need to observe that displacement is proportional and not equal to square of time. the proportionality constant has be converted into an equal to sign. Galileo used his knowledge of Eudoxu's theorem of proportions, a geometric method, described by Euclid (300 BC) in his book Elements. In the process, Galileo also seems to have been the first to use geometric construct to visualize space and time (displacement along y-axis and time along x-axis ). Amazing!
The moral of the story. To discover something, Start worrying (there are millions of problems to worry about. we just need to choose one :-) )
Note:
- Galileo also ended up discovering an improved version (20x magnification) of the telescope in 1609 to study the problem of planetary motions.
- If Galileo had lived longer, we would have even solved the problem of "What is matter made of". Looks like someone else started worrying about this problem and invented a microscope in 1620's.
- Momentum is yet to be associated with an inventors name. Force is in Newtons, Work is in Joules, Power is in Watts, not sure why momentum, which is inferred from the "law of inertia" was not given an inventors name? Oh. No more questions. Hence forth, let us measure momentum in "Galileo's"
References:
1. http://galileo.rice.edu/sci/instruments/pendulum.html
2. http://www.juliantrubin.com/bigten/galileofallingbodies.html
3. https://en.wikipedia.org/wiki/Pendulum
4. https://en.wikipedia.org/wiki/Seismometer
5. https://en.wikipedia.org/wiki/Foucault_pendulum
6. http://galileo.rice.edu/sci/instruments/telescope.html
7. http://www.mayowilson.org/Teaching/Files/philmath/Lectures/7_Lecture_Philmath.pdf
Some interesting videos then and now.
Time Estimate for Reading: 30 min
Learning Objectives: Introduction to displacement, velocity and acceleration
Effort Required: Medium
Pedagogy Model: Evolution
Prior Physics Concepts: Nil
Prior Math Tools: Secondary school level Arithmetic, geometry and algebra
The simple pendulum is one of the simplest and most important discoveries (1602) in science. It is simple for its construction; just a mass and a string.
For such a simple device, it is fascinating to see the wide range of applications it has been put to use:
- Gravimeter (1620)
- Clock (1656)
- Measure density of earth (1737)
- Standard for length (1791)
- Proof that earth is spinning: Foucault's pendulum (1851)
- Horizontal Pendulum: Seismograph (1880)
Even more important is the process of discovery having a rich history and spans almost 2000 years; Starting from Aristotle (350 BC) to 1602 (the Galilean era)As the famous story goes, Galileo happens to visit a cathedral in pisa (1588), observes a swinging chandelier and discovers a pendulum. Interestingly, 14 years seems to have passed between observation of swinging mass and discovering the pendulum.
The interesting question we may raise here is "When so many people visiting the church saw only the chandelier, why did it happen that only Galileo saw it as a pendulum?"
Lets us trace the interesting history by setting our clock to the times of Aristotle (350 BC) and attend a class on the law of falling bodies. This is what we would have been taught.
-
the substances making up the Earth were
different from the substance making up the heavens
-
He also taught that dynamics (the branch of
physics that deals with motion) was primarily determined by the nature of the
substance that was moving.
o
a stone fell to the ground because the stone and
the ground were similar in substance (in terms of the 4 basic elements, they
were mostly "earth")
o
smoke rose away from the Earth because in terms
of the 4 basic elements it was primarily air (and some fire), and therefore the
smoke wished to be closer to air and further away from earth and water
o
the more perfect substance (the "quintessence")
that made up the heavens had as its nature to execute perfect (that is, uniform
circular) motion
-
objects only moved as long as they were pushed.
o
objects on the Earth stopped moving once applied
forces were removed
o
the heavenly spheres only moved because of the
action of the Prime Mover (see picture depicted as being pushed by angels), who continually applied the force to the outer
spheres that turned the entire heavens
 |
 |
Now fast forward to the Galilean Period. 1580's.
Out of the million problems on hand (there are problems every where and every one has some problem or the other to worry about. It is only human to keep worrying), Galileo finds Aristotelian views to be interesting problems to worry upon. The view on what is matter made of?, Is earth at the center of everything? (may be because humans are the most important creatures in the universe!) and Whether bodies of different masses fall at the different rates (referred to as law of falling bodies)?
Given these three problems, the question is which one to prioritize and worry about?
1. The planets are too far away and only device known is human eye
2. On a similar and contrary note, to understand what is matter made off, we enter the regime of things that are too small for the human eye
3. The law of falling bodies "seem" to be the simplest of the three to work on and we choose to begin with this.
Having chosen the problem, we wish to know who else were interested in similar problems and find that, starting from Archimedes (250 BC), Da Vinci (1470) have observed that the bodies of different masses fall the same rate (contrary to Aristotelian beliefs)
A further analysis shows that
- In 1576, Giuseppe Moletti, Galileo's predecessor in the chair of mathematics at the university of Padua, reported that bodies of the same material but different weight, as well as bodies of the same volume but different material, dropped from a height arrived at the Earth at the same time.
- In 1586 (3 years before Galileo), Simon Stevin reported that different weights fell a given distance in the same time. His experiments, with the help of his friend Jan Cornetts de Groot, were conducted using two lead balls, one being ten times the weight of the other, which he dropped thirty feet from the church tower in Delft. from the sound of the impacts they concluded that the spheres fell with the same speed, not as stated by Aristotle. Stevin is regarded by many as the first one to perform falling bodies experiments.
Galileo being a mathematician and a man of experiments, finds that there are no quantitative measurements being made. Though others have observed and described that bodies fall at the same rate, no one seemed to have analysed (come up with a formula for) acceleration and time taken for the fall.
The seemingly simple problem was found difficult at that time because the bodies fall at a very fast rate. It would have covered approx (i have considered a value of 10 for acceleration) 5 meters in 1 second, 20 meters in 2 seconds and 50 meters in the third second etc. The time keepers of those days were the sun, the moon, the stars and the best of them all; the water clocks ( check this video on using water clock https://www.youtube.com/watch?v=ZUgYc6Bi46w
5.27 min ) were not sufficient enough to measure seconds and sub seconds.
So what do we do now? A seemingly simple problem poses a new challenge of time measurement. The options
- drop things from greater and greater heights (possible but not practical)
- invent a clock that can provide more resolution
Is there an alternate way to measure time? May be measure the pulse or take assistance from an expert musician to check the interval and offer a qualitative assessment (check this video on using sound/music https://www.youtube.com/watch?v=7HUj7obvKpA 4.10
min). Use of music does not however provide a quantitative measurement.
Is there an alternate way to increase the time of travel, without taking the ball to greater heights (Never Ever Give Up)? The rolling ball on an inclined plane might work. Inclined plane was one of early inventions, mainly used as a lever to gain mechanical advantage. May be Galileo got the idea of inclined planes after seeing the leaning (inclined) tower of Pisa. So, we need not get into speculation of whether Galileo really climbed Pisa Tower.
The inclined plane experiments offer a new set of problems. One of the problems leads to newtons 1st Law (yes, newton's first law, the law of inertia was actually discovered by Galileo) and the other leads to discovery of pendulum. One leading to the other.
A slope of 5 degrees seem to provide maximum travel time and the formula is arrived at connecting position and time; for the first time. distance traveled is proportional to the square of the time of fall.Here again we need to observe that displacement is proportional and not equal to square of time. the proportionality constant has be converted into an equal to sign. Galileo used his knowledge of Eudoxu's theorem of proportions, a geometric method, described by Euclid (300 BC) in his book Elements. In the process, Galileo also seems to have been the first to use geometric construct to visualize space and time (displacement along y-axis and time along x-axis ). Amazing!
The major challenge in constructing this equipment would have been in reducing friction. The inclined plane and the ball had to be polished to perfection for obtaining consistent results.
The possible answer to the question of why only Galileo sees pendulum and others see a chandelier?
With the problem of reducing friction in mind, Galileo looks at his past experience and predicts that the configuration of the chandelier; hanging from a single point of support might solve his friction problem and there he finds the pendulum.
A guess of how this inclined plane would have lead Galileo to the "Law of Inertia".
Let us assume that the balls when rolled down the plane would have run away from the base and collection of the same would have been a problem. So, a simpler solution would have been to place an obstacle. But this would create an impact on the ball and would result in noise and might damage the surface of the ball.
So, a better solution is to create a trough.
Experimenting with this trough leads to another observation that the height of release of ball and the height reached by the ball, seems to be more or less same; independent of the angle inclination.
Extending in this line of reasoning, Galileo raises another question. If the ball raises to the same height, independent of the inclination, what will happen if the angle of inclination is zero? The answer is the ball will try to reach the same height and will keep on rolling (in the absence of friction) and that is the "law of inertia".
Note:
- Galileo also ended up discovering an improved version (20x magnification) of the telescope in 1609 to study the problem of planetary motions.
- If Galileo had lived longer, we would have even solved the problem of "What is matter made of". Looks like someone else started worrying about this problem and invented a microscope in 1620's.
- Momentum is yet to be associated with an inventors name. Force is in Newtons, Work is in Joules, Power is in Watts, not sure why momentum, which is inferred from the "law of inertia" was not given an inventors name? Oh. No more questions. Hence forth, let us measure momentum in "Galileo's"
References:
1. http://galileo.rice.edu/sci/instruments/pendulum.html
2. http://www.juliantrubin.com/bigten/galileofallingbodies.html
3. https://en.wikipedia.org/wiki/Pendulum
4. https://en.wikipedia.org/wiki/Seismometer
5. https://en.wikipedia.org/wiki/Foucault_pendulum
6. http://galileo.rice.edu/sci/instruments/telescope.html
7. http://www.mayowilson.org/Teaching/Files/philmath/Lectures/7_Lecture_Philmath.pdf
Some interesting videos then and now.
- https://www.youtube.com/watch?v=MpzaCCbX-z4 8.45 min The discovery of pendulum
- https://www.youtube.com/watch?v=LJsFt1M3BV4 3 min Inclined plane experiment
- https://www.youtube.com/watch?v=7HUj7obvKpA 4.10 min Using sound/music
- https://www.youtube.com/watch?v=yc-FPEnp8Gg 1.00 min yale experiment
- https://www.youtube.com/watch?v=ZUgYc6Bi46w 5.27 min using water clock
- https://www.youtube.com/watch?v=2HR5UmG0q0s 3.00 min reconstructed pisa tower
- https://www.youtube.com/watch?v=AYz_K3mwq6A&ebc=ANyPxKr2TOLIo6VLRy9Z8rq49ELPJJ5qYvaLeT4_yk2pJ5O88iNAHu7-bM9MkDBH1cwTIAP3SsKQLYhYuYyYobflWFhh8XRqyw 5.5 min pillow and cooker
No comments:
Post a Comment