2 edition of Results of Captain Kater"s experiments for determining the length of the pendulum found in the catalog.
Results of Captain Kater"s experiments for determining the length of the pendulum
|Series||Landmarks of science II|
|Contributions||Kater, Captain 1777-1835.|
|LC Classifications||Q111 .H35, QB334 .H35|
|The Physical Object|
|Number of Pages||325|
Comparison of Eqs. (1) and (16) shows that the length l of the equivalent simple pendulum is l = h 1 + h 2 (17) Thus, the length of the equivalent simple pendulum is SO (Figs. 1 and 2). S’ and O’ are a second pair of conjugate points symmetrically located with respect to S and O respectively, i.e., having the same numerical values of h 1. Kater’s pendulum is a compound pendulum, in which the pendulum's centre of gravity don't have to be determined, allowing greater accuracy. 9. Kater knew that for the pendulum equation to be precise he needed to know the pendulum’s I.
1) Use the slope of the graph of τ vs. vL to calculate g. Compare your result with cm/sec2. 2) For one of your measurements calculate the angular acceleration (α) at the starting angle θo, at θ = 0, and at the far end of the swing. 3) Estimate the period of a pendulum, the length of . pendulum is given by: g L T = p or. 2 2 1 L g T S (eq. 1), where g is the acceleration due to gravity, m/s2. Equation 1 indicates that the period and length of the pendulum are directly proportional; that is, as the length, L, of a pendulum is increased, so will its period, T, .
2 Simple Pendulum Objective of this experiment Theory tells us that the behavior of a simple pendulum can be approximated by that of a simple harmonic oscillator for small amplitudes. Our goal is to determine for what initial displacement θ0 do we begin to measure a noticeable deviation from the approximation used in the theory. Theory. Experiment 14 The Physical Pendulum The period of oscillation of a physical pendulum is found to a high degree of accuracy by two methods: theory and experiment. The values are then compared. Theory For a rigid body that is constrained to rotate about a fixed axis, the gravitational torque about the axis is.
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A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in for use as a gravimeter instrument to measure the local acceleration of 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.
1 The reversible pendulum was first used to measure g by Captain Henry Kater: H. Kater, Philos Trans Roy Soc London33 (). 2 B. Crummett, The Physics Teac (). 3 Sargent-Welch Scientific model 4 It's length was measured by the machine shop that made it and has the value " stamped on its side. Get this from a library.
Remarks on Captain Kater's paper: containing experiments for determining the length of the second's pendulum in the latitude of London.
[William Watts]. Aim. To determine g, the acceleration of gravity at a particular location. Apparatus. Kater's pendulum, stopwatch, meter scale and knife edges.
Theory. Kater’s pendulum, shown in Fig. 1, is a physical pendulum composed of a metal rod m in length, upon which are mounted a sliding metal weight W 1, a sliding wooden weight W 2, a small sliding metal cylinder w, and two sliding knife.
amplitude, as long as the pendulum keeps covering the beam while it reverses its trajectory. Procedure: In this experiment in order to find g, first we need to determine the equivalent length: H º» ; å. Throughout the experiment sleeve A is fixed at a distance of 7 – 10 cm from one end of the pendulum.
Position of sleeve B can be. Kater Pendulum Introduction It is well-known result that the period T of a simple pendulum is given by T L g =2π where L is the length. In principle, then, a pendulum could be used to measure g, the acceleration of gravity.
However, practical difficulties—primarily in measuring the length. Kater's reversible pendulum. 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.
Moreover, the pendulum is provided with wedge-shaped knives O 1 and O 2, so that we can hang it on a vertical rigid. should derive this result on your own). g = 4π²L/T2 (3) 1. Measure the length of the pendulum to the middle of the pendulum bob.
Record the length of the pendulum in the table below. With the help of a lab partner, set the pendulum in motion until it completes 30 to and fro oscillations, taking care to record this time. Then the period T. SIMPLE PENDULUM EXPERIMENT Inference: how can you compare the theoretical results to the measured experimental.
Reply Delete. why is it necessary to add the radius of the bob to the length of the string to know the length of the pendulum?.
Reply. Experiment with Kater's Pendulum. The Kater pendulum is a gravimeter, an instrument used to measure the acceleration of gravity anywhere on. Procedure Real Lab. Shift the weight W 1 to one end of katers pendulum and fix it. 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.
Keep the small weight 'w' near to centre. Suspend the pendulum about the knife edge 1 and take the time for about 10 oscillations. Homework Statement Hey guys, so I'm doing the an exercise on the Kater's pendulum, to calculate g. I've gotten down my g calculation to g = m +/- using equation 1 below.
The errors taken into account are just on the kater period T. strictly applies only to a true simple pendulum, consisting of a point mass swinging on a massless rod or string. For a real, or physical, pendulum, the period is given as T =2p s I mgl: (2) Here, I is the moment of inertia of the pendulum about the pivot point, m is the pendulum’s mass, and l is the distance from this pivot to the center of.
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 period. These results can be checked against () (1 sin2 2)) 4 1 0 T α=T + α (where α is the angle of oscillation), as derived from the rigorous equation of motion.
Task 3 – Reporting. Account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London; Philosophical Transactions, vp; Reproduction in laboratory Resource Centre).
CHECK REFERENCE It is easy to see, in principle, that g can be measured by timing the period (T) of a simple pendulum and measuring its length (L. In this experiment, it looks as if we systematically used a length for the pendulum that was too short.
If 1 cm was added to our data, we would get a value for ‘g’ that is. for 20 complete oscillations by using a stopwatch. Repeat 10 times for each pendulum length.
Keep θ max at or below 20°. 𝜃For one length of pendulum, measure 1 set of 20 periods at à𝑎 =5 °,Compare your results to the model, 𝑇(𝜃 à𝑎)=𝑇0(1+ 1 4 𝑖 2𝜃𝑚𝑎𝑥 2 +9 64 𝑖 4𝜃𝑚𝑎𝑥 2. The Simple Pendulum Revised 10/25/ 6 2 2 4π T= g l.
(8) If the theory is correct, a graph of T2 versus l should result in a straight line. Square the values of the period measured for each length of the pendulum and record. The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ 0, called the amplitude.
It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is. The length of the pendulum should take into account hook, sring length, and radius of the bob.
The sring should not be streched too much while measuring its length.In this experiment we investigated the dependence of the period pf a pendulum on two variable, the mass of the bob and the length of the string. We followed the instructions and tried to keep the amplitude constant for all the measurements so that it would not affect the result, because we learned in class that in the case of a pendulum, large.case of deriving the value of g from measurements of the length and period of a pendulum in order to estimate the accuracy with which the measurements need to be made to achieve a result for g accurate to They discover that (σ g/g) 2 = (σ l/l) 2 + 4(σ T/T) 2 (3) which means that the pendulum length measurement needs to be accurate to.