This makes it easier to determine the local acceleration due to gravity from the period of oscillation and the reduced pendulum length. Am2 katers reversible pendulum lock haven university. M n1 l1 c l2 n2 n1 1 mg 2 d dt 2 sin i1 1 n1 d 2 mgl1 0 i1 dt 2 parallel axis b. Katers pendulum physics 258259 katers reversible pendulum is used to complete a precision measurement of the local acceleration of gravity in storrs connecticut.
In 1815 captain henry kater 17771835 devised a reversible physical pendulum design, and a data analysis method that improved the precision of determination of gravitational field strength by a factor of 10 to 100. Katers reversible pendulum steel cp rs 2,490 piece get latest price it is a compound pendulum constructed on the principle that centre of oscillation and centrenof suspension are interchangeable. Katers pendulum full explanation determination of g. The reversibility of point o and p described above is the principle of the reversible pendulum, invented by kater to measure gravity with high 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. Fix the brass weight w1 near one end of the kater s pendulum 5 cm from end 1 and the knife edge k1 just below it at a distance of about 2 cm. Rating 1 the reversible pendulum was first used to measure g by captain henry kater.
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. In 1815, henry kater developed a reversible pendulum, with which he could make measurements of g to unprecedented accuracy. Suppose the distances d1 and d2 are adjusted so that the periods around both supports are equal. Kater s pendulum should yield a value precise to three significant figures. An important application of the pendulum is the determination of the value of the acceleration due to gravity.
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. As a specialized manufacturer, exporter and supplier of laboratory instruments, we are serving the specific demands of clients by offering reversible pendulum. What is the difference between a simple pendulum and a. Katers pendulum is an example of compound pendulum, which is used to determine the value of g and has many other applications. Special form of physical pendulum for determining local acceleration due to gravity g. View docx from phys 101 at national taiwan university. Reversible kater s pendulum simple harmonic motion oscillations gravitational acceleration what it shows. Previous question next question get more help from chegg. 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. Reversible pendulum, physics of the pendulum, ma thematics of the pendulum pacs 2003. Introduction katers pendulum consists of a long bar and two masses which are attached to the bar. A pendulum is an object that is pivoted about a point other than its center of mass that is. Similarly, adjust the wooden weight w2 and the knife edge k2 at the other end end 2.
The pendulum is suspended from very lowfriction needle bearings on a stable support. 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 offered pendulum is precisely manufactured by our dexterous professionals using pristine quality metal alloys and stateofart techniques as per international quality standards. A pendulum consists of an object suspended along an axis so that it is able to move back and forth freely. For the computation to be physically reversible, and therefore not dissipate any energy, the computing engine must be logically reversible and implemented in a physically reversible. The pendulum can oscillate on either of two knifeedge suspension. The pendulum shown lying down, above is hung vertically and pivots on a knife edge that rests on glass. Its advantage is that, unlike previous pendulum gravimeters, the pendulum s centre of gravity and center of oscillation dont have to be determined, allowing greater accuracy. A simple pendulum hanging from a point suspension is in reality a twodimensional pendulum 123 4 5.
Determine the middle point of the rod and fix the smaller metal weight w there. We also discuss a real compound kater pendulum that realizes this property. Determine the period of oscillation and calculate the local acceleration due to gravity. Katers reversible pendulum used in this experiment has a knifeedge for suspension at. A kater pendulum, also known as a reversible pendu. 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. The following formula is used for the determination of acceleration due to gravity g. The pendulum rod has two fulcras as well as one sliding and one fixed disc to adjust the period of oscillation. Pdf the cubic perioddistance relation for the kate reversible. The principle of reversible katers pendulum and why its. For the physical pendulum experiment when the mass. 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. When the mass distribution of the pendulum is adjusted so.
Suspend the pendulum about the knife edge 1 and take the time for about 10 oscillations. Pendulum rod with two fulcra plus one sliding and one fixed disc. Measurement of the acceleration of gravity using katers. 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. It does so by counting cycles of a 1 mhz quartz crystal oscillator. Work out the local acceleration due to gravity with the help of a reversible pendulum. The reversible pendulum is a pendulum that can be swung from either of two pivot points. One of the most important physical constants is g, the.
The period of a physical pendulum depends on the moment of inertia of the device which, in practice, is almost impossible to determine accurately. After two centuries, still the most elegant determination of g. 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. View notes b6 katers reversible pendulum from phy 5 at university of toronto. The objective is to compare the value and accuracy of g using each pendulum in turn.
A kater pendulum, also known as a reversible pendulum, is constructed by attaching a counter weight to a long rod. A reversible pendulum is a special design of a normal physical pendulum. In 1817, british physicist henry kater developed a reversible pendulum which allows one to precisely measure the local acceleration due to. Set up katers pendulum, making sure it swings freely. In 1817 the english physicist henry kater, building on the work of the german astronomer friedrich wilhelm bessel, was the first to use a reversible pendulum to make absolute measurements of g. Reversible katers pendulum harvard natural sciences. If the periods of swing of a rigid pendulum about two alternative points of support are the same. Kater pendulum the pendulum can oscillate about a knife edge through either hole. 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. The bessel pendulum is a reversible pendulum that eliminates atmospheric corrections that apply to the more familiar kater pendulum. A physical pendulum with two adjustable knife edges for an accurate determination of g. 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.
For about a century, until the 1930s, kater s pendulum and its various refinements remained the standard method for. It generates a signal a tick each time the lower end of the pendulum swings through it. Adjustment of katers reversible pendulum for equal periods of oscillation. By adding a second knifeedge pivot and two adjustable masses to the physical pendulum described in the physical pendulum. The katers reversible pendulum is a special form of physical pendulum designed to determine the acceleration in response to gravity. Then it can be shown that this period is the period of a simple pendulum with. Bessels improved kater pendulum in the teaching lab. In 1817, british physicist henry kater developed a reversible pendulum which allows one to precisely measure the local acceleration due to gravity. 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. Laboratory physics, a students manual for colleges and scientific schools. Experiment katers reversible pendulum introduction. A1 is taken from kaye and laby online where the accuracy of the expression is also discussed. Empirical value for g the acceleration due to gravity at the surface of the earth can be approximated to the empirical expression a1 and depends on latitude and height above sea level.
To adjust horizontal orientation, the support is equipped with two adjustment screws and a level. The periods when the pendulum is swung from each of the pivots are recorded. Find out information about katers reversible pendulum. Pdf we describe the correct cubic relation between the mass configuration of a kater reversible pendulum and its period of oscillation. 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. 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 countertimer precisely measures the time duration of 8, 16 or 32 full periods of the pendulum. Shift the weight w 1 to one end of katers pendulum and fix it. Bessel and his version can be demonstrated with this equipment.
The holes are located so that the two periods of oscillation are nearly equal. Kater s key breakthrough was to use a pendulum that could be swung from either of two pivots, located at opposite ends of the pendulum. Katers pendulum consists of a long bar, equipped with two. Each of the sliding objects can be clamped in place on the rod. Reversible katers pendulum harvard natural sciences lecture. It is a compound pendulum constructed on the principle that centre of oscillation and centre of suspension are interchangable. Why is it that, when using a katers pendulum where the pivot points are fixed and one weight is adjustable, it is acceptable to discard the factor of the difference between the two distances of the individual pivot points from the center of gravity 1l1l2 in the following formula.
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