A special reversible compound pendulum called katers pendulum is designed to measure the value of g, the acceleration of gravity. The reversible pendulum is a pendulum that can be swung from either of two pivot points. And since the individual displacements are not known we actually know, via measurement, their sum, then our formula is actually 2 2. Kater pendulum theoretical considerations randall d.
Its experimental setup procedure involved and applications of katers pendulum. Join us on facebook download the experiment from the link be. A pendulum is a weight suspended from a pivot so that it can swing freely. Analysis graph of time taken for 10 complete oscillations versus length of simple pendulum. A gravity pendulum designed to measure the acceleration of gravity and consisting of a body with two knifeedge supports on opposite sides of the center of mass explanation of katers reversible pendulum.
The simple pendulum the university of tennessee at. This is a weight or bob on the end of a massless cord suspended from a pivot, without friction. The objective is to compare the value and accuracy of g using each pendulum in turn. However, a real pendulum is not a simple pendulum, and the effective length le of a real pendulum can be difficult to define. The katers pendulum works as a reversible and adjustable compound pendulum. Mercer university macon, georgia 31207 with the information provided in this article, students should be able to easily measure the acceleration of gravity to a few parts in tenthousand in one twohour laboratory period. Moment of inertia with respect to the axis of oscillation ao.
The equipment is a model of a socalled reversion pendulum. A katers pendulum is a reversible free swinging pendulum invented by british physicist and. It is able to swing from either of two mounting points and can be set up in such a way that the period of oscillation is the same from both these points. The simplest form of the kater pendulum is as shown. Homework statement hey guys, so im doing the an exercise on the katers pendulum, to calculate g. A compound pendulum has an extended mass, like a swinging bar, and is free to oscillate about a horizontal axis. After two centuries, still the most elegant determination of g. Measurement of the acceleration of gravity using katers.
Bessel in 18264 is apparently much less familiar to present date physicists. One can eliminate the dependence of the period of a physical pendulum on i by using a katers pendulum, which is a physical pendulum that has a pivot point a knife edge on each end. Nowadays pendulum mechanisms are more often used in. The katers pendulum is used to measure the acceleration due to gravity more accurately. Heuristic objectives to show what is involved in making a high precision measurement of an unknown quantity. Measurement of moment of inertia of different bodies and proof of parallel. A katers pendulum is a reversible free swinging pendulum invented by british physicist and army captain henry kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. The principle of reversible katers pendulum and why its rods ends are pointed. The simple pendulum is a favorite introductory exercise because galileos experiments on pendulums in the early 1600s are usually regarded as the beginning of experimental physics. Katers pendulum konstantinos filippakos the use of. A simple pendulum consists of a small bob suspended by a light massless string of length l. We describe a bessel pendulum for use in the teaching laboratory, and measurements of the local. It is a compound pendulum constructed on the principle that centre of oscillation and centre of suspension are interchangable. The pendulum sits on one of two knifeedged pivots that is attached to the.
Experiment for studying simple harmonic motion and the factors that affect the period of oscillation of pendulums. Help with determining errors on katers pendulum experiment. The pendulum is an exquisitely simple divination tool that is used for discovering information outside of our normal awareness. When the pendulums center of mass is below the pivot, the pendulum is in a equilibrium point i. The wider the gap in the crutch wire the longer it takes the crutch to catch up to the pendulum rod.
The katers pendulum consists of a rigid metal bar with two pivot points, one near each end. The principle of reversible katers pendulum and why its. To understand what he did, we will first look at simple pendula and then we will develop katers. The katers reversible pendulum is made of a rigid metal bar on which are inserted two massive discs m 1 and m 2 that can scroll along the bar and be fixed in different positions in order to change the position of center of gravity of the pendulum. Find out information about katers reversible pendulum.
Katers pendulum full explanation determination of g. The errors taken into account are just on the kater period t and the distance between the two pivot points l. The final part of the experiment is to measure the validity of this approximation by varying the amplitude of oscillation of katers pendulum and recording the. The cubic perioddistance relation for the kater reversible pendulum. Katers pendulum since at least 1965, the cavendish laboratory physics course included an experiment to measure g to better than 1 part in 10,000 using katers pendulum. The reversion pendulum was developed by henry kater. A clever improvement to the kater pendulum devised by. In 1817, kater, following a suggestion from bessel, developed a reversible pendulum that made possible an extremely accurate measurement of the acceleration due to earths gravity, g.
When released, the restoring force acting on the pendulum s mass causes it to oscillate about the equilibrium position. The simple pendulum university of colorado boulder. The time taken for the pendulum to increase make one complete oscillation will when the 9. With 2012 looming in the not so distant future and bearing down on us rapidly, our ability to create safe environments for. Background katers pendulum is the name given for a reversible swinging pendulum first invented by the british physicist henry. Katers reversible pendulum mechanics oscillations objective work out the local acceleration due to gravity with the help of a reversible pendulum ue1050221 ue1050221 basic principles a reversible pendulum is a special design of a normal physical pendulum. In practice, the movable mass is divided into two or more elements to enable coarse and fine adjustment. Its advantage is that, unlike previous pendulum gravimeters, the pendulum s centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. Pendulums have played an important role in the history of dynamics. String, pendulum bob, meter stick, computer with uli interface, and a photogate. Reversible katers pendulum harvard natural sciences. Katers pendulum is a pendulum that consists of a steel arm with a length of about one and a half meters. If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum.
Be sure that the pendulum swings straight through the gate. For about a century, until the 1930s, katers pendulum and its various refinements remained the standard method for. A physical pendulum is a rigid body swing in a vertical plane about any horizontal axis passing. The positions of m1 and m2 along the bar are adjusted until the period of oscillations t1 around ao1 is equal to the period of oscillation t2 around ao2. The general formula of the time period for bar pendulum is given by following equation. To determine the value of g at niser using a reversible pendulum. Peters department of physics mercer university macon, georgia 31207 1 idealized kater pendulum consider a uniform rectangular pendulum as illustrated in figure 1. Umberto eco foucalts pendulum only for you, children of doctrine and learning, have we written this work. The period for this arrangement can be proved 2 to be the same as that of a simple pendulum whose length l is the distance between the two knife edges. Our experiment may be similar to one you have done in high school, however, the mathematical analysis will be more. The other two pendulums will yield far less precise values and it is important to determine the errors for each pendulum to allow a discussion of the precision of the values of g. Moreover, the pendulum is provided with wedgeshaped knives o 1 and o 2, so that we can hang it on a. Bessels improved kater pendulum in the teaching lab d. Each of the sliding objects can be clamped in place on the rod.
To investigate the relationship between the length of a simple pendulum and the period of its motion. When given an initial push, it will swing back and forth at a constant amplitude. Purpose in this experiment, we use a kater pendulum to measure the acceleration due to gravity, g, in our location in seattle, wa, and compare it to the accepted value, as well as the value we obtained in our previous experiment with the simple pendulum. Too much play and the crutch loop will have to travel too far to catch up to the swinging pendulum before imparting impulse. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. To determine the value of acceleration due to gravity and radius of gyration using bar pendulum.
It is able to swing from either of two mounting points and can be. Reversible katers pendulum harvard natural sciences lecture. Katers innovation was to realize that, if one built an asymmetrical, doubleended pendulum as is shown schematically in fig. Simple and compound pendulums tm161 experiment simple and compound pendulums.
A physical pendulum with two adjustable knife edges for an accurate determination of g. Langley physics department, university of massachusetts, amherst, massachusetts 01003 received 9 november 2000. What it shows an important application of the pendulum is the. The following formula is used for the determination of acceleration due to gravity g. Real pendulums are subject to friction and air drag, so the amplitude of their swings. Related threads on the principle of reversible katers pendulum and why its rods ends are pointed katers pendulum. Experimentally, kater s pendulum was used to accurately measure the local acceleration of gravity.
Turner apr 8, 2009 in 1817, british physicist henry kater developed a reversible pendulum which allows one to precisely measure the local acceleration due to gravity. Its advantage is that, unlike previous pendulum gravimeters, the pendulums centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. The reversible pendulum kater s pendulum has two pivot points on opposite sides of the centre of gravity from which the pendulum can be suspended as shown in fig. Katers pendulum stuart field and eric hazlett abstract in this lab we will determine the value of the acceleration of gravity g by using a reversible pendulum. It has a large mass near the end on one side, and a small her mass near the other end. The simple gravity pendulum is an idealized mathematical model of a pendulum. The pendulum shown lying down, above is hung vertically and pivots on a knife edge that rests on glass. The period of a physical pendulum depends on the moment of inertia of the device which, in practice, is almost impossible to determine accurately. Lecture l24 pendulums a pendulum is a rigid body suspended from a. Around 1817, henry kater used a reversable pendulum now called a katers pendulum to make extremely accurate measurements of the acceleration due to gravity to simplify a little. The pendulum with a longer string longer takes time to oscillate than the pendulum with a shorter string. This is why the kater reversible pendulum is one of the favourite instruments for.
In principle, then, a pendulum could be used to measure g, the acceleration of gravity. Bessels improved kater pendulum in the teaching lab. Examine this book, ponder the meaning we have dispersed in various places and gathered again. Katers pendulum is an example of compound pendulum, which is used to determine the value of g and has many other. The katers pendulum used in the instructional laboratories is diagramed below and its adjustments are described in the setting it up section. We describe a bessel pendulum for use in the teaching laboratory, and measurements of the local acceleration of gravity made with it to an accuracy of better than one part in 104.
This results in the pendulum receiving an abrupt hit late in its oscillation rather than a full. To verify the acceleration due to gravity using a katers pendulum. Kater s pendulum should yield a value precise to three significant figures. Katers pendulum definition is a compound pendulum with adjustable knife edges placed respectively at the center of suspension and near the center of oscillation and used to determine acceleration of gravity by means of the period of oscillation.
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