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. 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. After two centuries, still the most elegant determination of g. Katers innovation was to realize that, if one built an asymmetrical, doubleended pendulum as is shown schematically in fig. The pendulum is to be suspended from two different points of suspension defined as 01 and 02. It was often thought until now that the earlier period in the late 18th century only produced relative gravity measurements. Suppose the distances d1 and d2 are adjusted so that the periods around both supports are equal. Grading for the course is primarily based on these articles weighted roughly 5050 for writing and scientific treatment as reflected in the grading grid. In 1817, kater, following a suggestion from bessel, developed a reversible pendulum that made possible an extremely accurate measurement of the acceleration due to earth s gravity, g. Katers pendulum is a very highprecision method of measuring local gravitational field. Feb 16, 20 i am not able to think which pendulum is more better. Comparing the gravity at two different points was an easier process than measuring it absolutely by the kater method. Shift the weight w 1 to one end of katers pendulum and fix it.
For example, its hard to estimate where exactly the center of the mass is. The kater s 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. B6 katers reversible pendulum experiment katers reversible. It was thus demonstrated that a crude, low mass kater pendulum can do as well as a decent simple pendulum. For example, it s hard to estimate where exactly the center of the mass is. Katers pendulum konstantinos filippakos the use of katers. Reversible katers pendulum harvard natural sciences.
Katers pendulum konstantinos filippakos the use of. Introduction katers pendulum consists of a long bar and two masses which are attached to the bar. To overcome this difficulty we can turn a physical pendulum into a socalled reversible kater s 1 pendulum. Feb 15, 2015 homework statement hey guys, so im doing the an exercise on the kater s pendulum, to calculate g. The pendulum can oscillate on either of two knifeedge suspension points as shown in fig. The length of the pendulum is the independent variable and should be plotted on the horizontal axis or abscissa x axis. In principle, then, a pendulum could be used to measure g, the acceleration of gravity. Bessels improved kater pendulum in the teaching lab d. Two knifeedge pivot points and two adjustable masses are positioned on the rod so that the period of swing is the same from either edge. Kater pendulum college of saint benedict and saint johns. Amrita vishwa vidyapeetham virtual lab, 2015 your bibliography. Suspend the pendulum about the knife edge 1 and take the time for about 10 oscillations.
With this wooden pendulum, the periods were found to match from a linear least squares fit for the clips at 11. Fix the knife edge k 1 just below it keep the knife edge k 2 at the other end and fix the wooden weight w 2 symmetrical to other end. Theoretical katerscompoundreversiblependulumisbaseddi rectlyonhuyghensprinciplethatthecentersofoscillation andsuspensionareinterchangeable. The experiment of kater s reversible pendulum contains not only the principle basis of the pendulum, but also the concept of the angular moment of inertia of a rigid body, as well as the understanding of how to derive from a compound pendulum the relationship among the swing period, the amplitude, the angular moment of inertia, and the acceleration of gravity.
The pendulums main function is to determine a yes or no answer, to a properly phrased question. It is a compound pendulum constructed on the principle that centre of oscillation and centre of suspension are interchangable. View notes b6 kater s reversible pendulum from phy 5 at university of toronto. What it shows an important application of the pendulum is the determination of the value of the acceleration due to gravity. Both are compound pendulums and i think katers is better, but for what reasons, i am not sure. Kater s innovation was to realize that, if one built an asymmetrical, doubleended pendulum as is shown schematically in fig. This amounts to the knowledge of radius of gyration. The simple pendulum the university of tennessee at. One axis of rotation is an end, and we wish to find another axis for which the periods of oscillation about the two parallel axes. The experiment of katers reversible pendulum contains not only the principle basis of the pendulum, but also the concept of the angular moment of inertia of a rigid body, as well as the understanding of how to derive from a compound pendulum the relationship among the swing period, the amplitude, the angular moment of inertia, and the acceleration of gravity. 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. Measurement of the acceleration of gravity using katers. Ding 2 i will be investigating the effect of the length of a pendulums string on the time for the period of that pendulum. Bessels improved kater pendulum in the teaching lab.
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. 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. Langley physics department, university of massachusetts, amherst, massachusetts 01003 received 9 november 2000. Note that the pendulum must be turned upside down to oscillate about axis 2, the adjustable knife edge. 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. View notes b6 katers reversible pendulum from phy 5 at university of toronto. Experiment katers reversible pendulum introduction. Accurate gravity measurements are possible by using katers pendulum. To understand what he did, we will first look at simple pendula and then we will develop katers result. Measurement of the acceleration of gravity using katers pendulum. The pendulum shown lying down, above is hung vertically and pivots on a knife edge that rests on glass.
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. A special reversible compound pendulum called katers pendulum is designed to measure the value of g, the acceleration of gravity. Our pendulum can measure the value of g to at least three decimal places, and possibly five. Graph the period of the pendulum as a function of its length using the chart feature of excel. The physics of kater s pendulum consider a physical pendulum with unspecified distribution of mass m. The accurate measurement of g using kater s pendulum, u. The holes are located so that the two periods of oscillation are nearly equal. Kater introduced the idea of relative gravity measurements, to supplement the absolute measurements made by a kater s pendulum. To determine the value of g at niser using a reversible pendulum. A pendulum is a weight suspended from a pivot so that it can swing freely. Kater pendulum the pendulum can oscillate about a knife edge through either hole.
A physical pendulum with two adjustable knife edges for an accurate determination of g. Pendulum, body suspended from a fixed point so that it can swing back and forth under the influence of gravity. It has a large mass near the end on one side, and a small her mass near the other end. Katers pendulum should yield a value precise to three significant figures. When released, the restoring force acting on the pendulums mass causes it to oscillate about the equilibrium position. The errors taken into account are just on the kater period t and the distance between the two pivot points l using a vernier scale. Katers pendulum definition of katers pendulum by merriam. Kater s 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 kater s pendulum. Admiralty records, biots papers and very kind advice from mr and mrs david edmondston of buness. Kater s pendulum is a very highprecision method of measuring local gravitational field. Electronics and instrumentation 5 wks starting with fundamental measurements of resistance and simple voltage divider circuits, statistics is revisited and extended to include ttest for combination of multiple data sets. The apparatus consists of an aluminum bar in which are two preciselyspaced holes which serve as pivot points. The reversible pendulum katers pendulum has two pivot points on opposite sides of the centre of gravity from which the pendulum can be suspended as shown in fig.
To overcome this difficulty we can turn a physical pendulum into a socalled reversible katers 1 pendulum. Katers pendulum, an rcrl properties, viscosity or cavendish, and the final project. When the schuler pendulum is vertically suspended, it remains aligned to the local vertical even if the point from which it is suspended is accelerated parallel to earths. An absolute determination of the acceleration of gravity. By adding a second knifeedge pivot and two adjustable masses to the physical pendulum described in the physical pendulum demo, the value of g can be determined. The physics of katers pendulum consider a physical pendulum with unspecified distribution of mass m. Kater knew that for the pendulum equation to be precise he needed to know the pendulums i. One axis of rotation is an end, and we wish to find another axis for which the periods of oscillation about the two parallel axes are the same. Investigating the effect of string length on pendulum. It has been used to find buried land mines and tunnels during wartime, finding lost objects, finding people, finding ghosts, increasing your. Pendulums are used to regulate the movement of clocks because the interval of time for each complete oscillation, called the period, is constant. Moreover, the pendulum is provided with wedgeshaped knives o 1 and o 2, so that we can hang it on a. Pendulum in latin means hanging something hanging from a fixed point which, when pulled back and released, is free to swing down by force of gravity and then out and up because of its inertia. 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.
Hey guys, so im doing the an exercise on the katers pendulum, to calculate g. The pendulum sits on one of two knifeedged pivots that is attached to the wall and allows it to oscillate easily without much disturbance. Katers pendulum is a compound pendulum, in which the pendulums centre of gravity dont have to be determined, allowing greater accuracy. Combining writing, basic instrumentation, fundamental. It is able to swing from either of two mounting points and can be. The kater s pendulum is used to measure the acceleration due to gravity more accurately. Physics practical simple pendulum experiment duration.
We describe a bessel pendulum for use in the teaching laboratory, and measurements of the local. 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. 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. 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. The first absolute gravity observations in australia and. Given my previous knowledge, i know that a pendulum behaves in an. Kater pendulum introduction it is wellknown result that the period t of a simple pendulum is given by t l g 2. Theoretical kater scompoundreversiblependulumisbaseddi rectlyonhuyghensprinciplethatthecentersofoscillation andsuspensionareinterchangeable. A physical pendulum is a rigid body swing in a vertical plane about any horizontal axis passing. By adding a second knifeedge pivot and two adjustable masses to the physical pendulum described in the physical pendulum demo, the value of g can be determined to 0. Kater pendulum theoretical considerations randall d. Both are compound pendulums and i think kater s is better, but for what reasons, i am not sure. The reversible pendulum is a pendulum that can be swung from either of two pivot points. I am not able to think which pendulum is more better.
Peters department of physics mercer university macon, georgia 31207 1 idealized kater pendulum consider a uniform rectangular pendulum as illustrated in figure 1. First there is the fairly standard adjustment for nonlinearity, which means the period increases as the amplitude of the swing increases. With 2012 looming in the not so distant future and bearing down on us rapidly, our ability to create safe environments for. The errors taken into account are just on the kater period t and the distance between the two pivot points l. One of the most important physical constants is g, the. If the pendulum weight or bob is pulled to a relatively small angle from the vertical and let go, it will swing back and forth at a regular period and frequency. But when we look more closely, it is much more complex. The amplitude scale can be read with the pointers shown as e. However, practical difficultiesprimarily in measuring the length. The objective is to compare the value and accuracy of g using each pendulum in turn.
Then it can be shown that this period is the period of a simple pendulum with. Each of the sliding objects can be clamped in place on the rod. Katers pendulum is a pendulum that consists of a steel arm with a length of about one and a half meters. Investigating the effect of string length on pendulum period chunyang ding ib candidate number. To understand what he did, we will first look at simple pendula and then we. This article illustrates the very different talents and temperaments of biot and colby, while leaving the reader to judge the reasons for their disagreement, and it goes on to describe katers pendulum observations at buness, those by sabine.
In addition to the articles, a laboratory practical at the. Kater s 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. A simple pendulum consists of a point mass suspended on a string or wire that has negligible mass. Katers reversible pendulum is used to complete a precision measurement of the local acceleration of gravity in storrs connecticut. Help with determining errors on katers pendulum experiment. I year practical physics uttarakhand open university. The pendulum is an exquisitely simple divination tool that is used for discovering information outside of our normal awareness. Design and development of pendulum operated water pump. A reversible pendulum, knife edges, support stands, photodetectorstop watch, measuring tapescale.
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