determination of acceleration due to gravity by compound pendulum determination of acceleration due to gravity by compound pendulum
1 The reversible pendulum was first used to measure g by Captain Henry Kater: H. Kater, Philos Trans Roy Soc London 108, 33 (1818).2 B. Crummett, The Physics Teacher 28, 291 (1990).3 Sargent-Welch Scientific model 8124 It's length was measured by the machine shop that made it and has the value 17.9265" stamped on its side. The distance of each hole from the center of gravity is measured. We adjusted the knots so that the length of the pendulum was \(1.0000\pm0.0005\text{m}\). size of swing . Any object can oscillate like a pendulum. The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. If this experiment could be redone, measuring \(10\) oscillations of the pendulum, rather than \(20\) oscillations, could provide a more precise value of \(g\). This method for determining g can be very accurate, which is why length and period are given to five digits in this example. Formula: This correspond to a relative difference of \(22\)% with the accepted value (\(9.8\text{m/s}^{2}\)), and our result is not consistent with the accepted value. 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We first need to find the moment of inertia. Aim . gravity by means of a compound pendulum. An example of data being processed may be a unique identifier stored in a cookie. Find more Mechanics Practical Files on this Link https://alllabexperiments.com/phy_pract_files/mech/, Watch this Experiment on YouTube https://www.youtube.com/watch?v=RVDTgyj3wfw, Watch the most important viva questions on Bar Pendulum https://www.youtube.com/watch?v=7vUer4JwC5w&t=3s, Please support us by donating, Have a good day, Finally found the solution of all my problems,the best website for copying lab experiments.thanks for help, Your email address will not be published. Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia I = \(\int\)r2 dm times the angular acceleration \(\alpha\), where \(\alpha = \frac{d^{2} \theta}{dt^{2}}: \[I \alpha = \tau_{net} = L (-mg) \sin \theta \ldotp\]. In this experiment, we measured \(g=(7.65\pm 0.378)\text{m/s}^{2}\). By adding a second knife-edge pivot and two adjustable masses to the physical pendulum described in the Physical Pendulumdemo, the value of g can be determined to 0.2% precision. Use a 3/4" dia. As with simple harmonic oscillators, the period T T for a pendulum is nearly independent of amplitude, especially if is less than about 15 15. A . Measurement of acceleration due to gravity (g) by a compound pendulum Aim: (i) To determine the acceleration due to gravity (g) by means of a compound pendulum. Manage Settings [] or not rated [], Copyright 2023 The President and Fellows of Harvard College, Harvard Natural Sciences Lecture Demonstrations, Newton's Second Law, Gravity and Friction Forces, Simple Harmonic (and non-harmonic) Motion. Even simple . Kater's pendulum, stopwatch, meter scale and knife edges. We also found that our measurement of \(g\) had a much larger uncertainty (as determined from the spread in values that we obtained), compared to the \(1\)% relative uncertainty that we predicted. In this video, Bar Pendulum Experiment is explained with calculatio. In difference location that I used to and Garin Arab has the lowest value of acceleration due to gravity which is (9.73m/s 2). Thus you get the value of g in your lab setup. Consider an object of a generic shape as shown in Figure \(\PageIndex{2}\). The corresponding value of \(g\) for each of these trials was calculated. This research work is meant to investigate the acceleration due to gravity "g" using the simple pendulum method in four difference locations in Katagum Local Government Area of Bauchi State. Legal. We thus expect to measure one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% relative uncertainty on the period). Pendulum 2 has a bob with a mass of 100 kg. An engineer builds two simple pendulums. We constructed the pendulum by attaching a inextensible string to a stand on one end and to a mass on the other end. You can download the paper by clicking the button above. The distance between two knife edges can be measured with great precision (0.05cm is easy). The object oscillates about a point O. The period of a simple pendulum depends on its length and the acceleration due to gravity. /F4 15 0 R To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. This will help us to run this website. The acceleration of gravity decreases as the observation point is taken deeper beneath the surface of the Earth, but it's not the location of the compound pendulum that's responsible for the decrease. /F10 33 0 R A physical pendulum with two adjustable knife edges for an accurate determination of "g". What should be the length of the beam? The following data for each trial and corresponding value of \(g\) are shown in the table below. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. Adjustment of the positions of the knife edges and masses until the two periods are equal can be a lengthy iterative process, so don't leave it 'till lecture time. Fair use is a use permitted by copyright statute that might otherwise be infringing. Consider the torque on the pendulum. The bar was displaced by a small angle from its equilibrium position and released freely. The consent submitted will only be used for data processing originating from this website. The net torque is equal to the moment of inertia times the angular acceleration: \[\begin{split} I \frac{d^{2} \theta}{dt^{2}} & = - \kappa \theta; \\ \frac{d^{2} \theta}{dt^{2}} & = - \frac{\kappa}{I} \theta \ldotp \end{split}\], This equation says that the second time derivative of the position (in this case, the angle) equals a negative constant times the position. 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\newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Example \(\PageIndex{1}\): Measuring Acceleration due to Gravity by the Period of a Pendulum, Example \(\PageIndex{2}\): Reducing the Swaying of a Skyscraper, Example \(\PageIndex{3}\): Measuring the Torsion Constant of a String, 15.4: Comparing Simple Harmonic Motion and Circular Motion, source@https://openstax.org/details/books/university-physics-volume-1, State the forces that act on a simple pendulum, Determine the angular frequency, frequency, and period of a simple pendulum in terms of the length of the pendulum and the acceleration due to gravity, Define the period for a physical pendulum, Define the period for a torsional pendulum, Square T = 2\(\pi \sqrt{\frac{L}{g}}\) and solve for g: $$g = 4 \pi^{2} \frac{L}{T^{2}} ldotp$$, Substitute known values into the new equation: $$g = 4 \pi^{2} \frac{0.75000\; m}{(1.7357\; s)^{2}} \ldotp$$, Calculate to find g: $$g = 9.8281\; m/s^{2} \ldotp$$, Use the parallel axis theorem to find the moment of inertia about the point of rotation: $$I = I_{CM} + \frac{L^{2}}{4} M = \frac{1}{12} ML^{2} + \frac{1}{4} ML^{2} = \frac{1}{3} ML^{2} \ldotp$$, The period of a physical pendulum has a period of T = 2\(\pi \sqrt{\frac{I}{mgL}}\). /Type /Page In this channel you will get easy ideas about Physics Practical Classes. As the pendulum gets longer the time increases. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Their value was stated to have and uncertainty of 0.003 cm/s2. There are many way of measuring this gravity acceleration, but the experiment of compound pendulum is the easiest and effective among them. The formula for the period T of a pendulum is T = 2 Square root of L/g, where L is the length of the pendulum and g is the acceleration due to gravity. Academia.edu no longer supports Internet Explorer. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12. https://alllabexperiments.com/phy_pract_files/mech/, https://www.youtube.com/watch?v=RVDTgyj3wfw, https://www.youtube.com/watch?v=7vUer4JwC5w&t=3s, V-I Characteristics of Diode, LED, and Zener diode lab manual. A 3/4" square 18" long 4 steel bar is supplied for this purpose. Using the small angle approximation and rearranging: \[\begin{split} I \alpha & = -L (mg) \theta; \\ I \frac{d^{2} \theta}{dt^{2}} & = -L (mg) \theta; \\ \frac{d^{2} \theta}{dt^{2}} & = - \left(\dfrac{mgL}{I}\right) \theta \ldotp \end{split}\], Once again, the equation says that the second time derivative of the position (in this case, the angle) equals minus a constant \(\left( \dfrac{mgL}{I}\right)\) times the position. 3 0 obj A string is attached to the CM of the rod and the system is hung from the ceiling (Figure \(\PageIndex{4}\)). /Contents 4 0 R When a physical pendulum is hanging from a point but is free to rotate, it rotates because of the torque applied at the CM, produced by the component of the objects weight that acts tangent to the motion of the CM. (ii) To determine radius of gyration about an axis through the center of gravity for the compound pendulum. We are asked to find the torsion constant of the string. The mass, string and stand were attached together with knots. In an experiment to determine the acceleration due to gravity, s, using a compound pendulum, measurements in the table below were obtained. Retort stand, boss head, and clamp, string and mass bob, Stopwatch, rulerif(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physicsteacher_in-box-4','ezslot_5',148,'0','0'])};__ez_fad_position('div-gpt-ad-physicsteacher_in-box-4-0'); Record the data in the table below following the instructions in the section above. Theory A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. , How to Calculate Acceleration Due to Gravity Using a Pendulum, Free Printable Periodic Tables (PDF and PNG), Periodic Table with Charges - 118 Elements. This looks very similar to the equation of motion for the SHM \(\frac{d^{2} x}{dt^{2}}\) = \(\frac{k}{m}\)x, where the period was found to be T = 2\(\pi \sqrt{\frac{m}{k}}\). The rod is displaced 10 from the equilibrium position and released from rest. ], ICSE, CBSE class 9 physics problems from Simple Pendulum chapter with solution, How to Determine g in laboratory | Value of acceleration due to gravity -, Simple Harmonic Motion of a Simple Pendulum, velocity of the pendulum bob at the equilibrium position, Transfers between kinetic & potential energy in a simple pendulum, Numerical problem worksheet based on the time period of pendulum, Acceleration, velocity, and displacement of projectile at different points of its trajectory, Satellite & Circular Motion & understanding of Geostationary Satellite. 1 Pre-lab: A student should read the lab manual and have a clear idea about the objective, time frame, and outcomes of the lab. This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format
Object: To determine the acceleration due to gravity (g) by means of a compound pendulum. As the skyscraper sways to the right, the pendulum swings to the left, reducing the sway. A compound pendulum (also known as a physical pendulum) consists of a rigid body oscillating about a pivot. The various results that I have found, reveals that the average value of acceleration due to gravity for Azare area of Katagum Local Government is 9.95m/s 2 which approximately equal to the accepted value of 10.0m/s 2. 4 2/T 2. The time period is determined by fixing the knife-edge in each hole. /F5 18 0 R Plug in the values for T and L where T = 2.5 s and L = 0.25 m g = 1.6 m/s 2 Answer: The Moon's acceleration due to gravity is 1.6 m/s 2. Sorry, preview is currently unavailable. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out. Set up the apparatus as shown in the diagram: Measure the effective length of the pendulum from the top of the string to the center of the mass bob. We can then use the equation for the period of a physical pendulum to find the length.
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