PDF Experiment 9: Compound Pendulum - GitHub Pages What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s? Here, the length L of the radius arm is the distance between the point of rotation and the CM. The restoring torque can be modeled as being proportional to the angle: The variable kappa (\(\kappa\)) is known as the torsion constant of the wire or string. To determine the radius of gyration about an axis through the centre of gravity for the compound pendulum. We expect that we can measure the time for \(20\) oscillations with an uncertainty of \(0.5\text{s}\). The bar was displaced by a small angle from its equilibrium position and released freely. >> Object: To determine the acceleration due to gravity (g) by means of a compound pendulum. determine a value of acceleration due to gravity (g) using pendulum motion, [Caution: Students are suggested to consult Lab instructors & teachers before proceeding to avoid any kind of hazard. We thus expect that we should be able to measure \(g\) with a relative uncertainty of the order of \(1\)%. Several companies have developed physical pendulums that are placed on the top of the skyscrapers. 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. The angular frequency is, \[\omega = \sqrt{\frac{mgL}{I}} \ldotp \label{15.20}\], \[T = 2 \pi \sqrt{\frac{I}{mgL}} \ldotp \label{15.21}\]. We repeated this measurement five times. 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. Even simple . This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds toupgrade your browser. /Parent 2 0 R [Caution: Students are suggested to consult Lab instructors & teachers before proceeding to avoid any kind of hazard.]. The distance between two knife edges can be measured with great precision (0.05cm is easy). Read more here. Theory. In this experiment the value of g, acceleration due gravity by means of compound pendulum is obtained and it is 988.384 cm per sec 2 with an error of 0.752%. This page titled 15.5: Pendulums is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The pendulum was released from \(90\) and its period was measured by filming the pendulum with a cell-phone camera and using the phones built-in time. The locations are; Rafin Tambari, Garin Arab, College of Education Azare and Township Stadium Azare. Like the force constant of the system of a block and a spring, the larger the torsion constant, the shorter the period. What should be the length of the beam? 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. 4 2/T 2. How to Calculate Acceleration Due to Gravity Using a Pendulum This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format
The mass, string and stand were attached together with knots. Aim . Consider a coffee mug hanging on a hook in the pantry. The minus sign is the result of the restoring force acting in the opposite direction of the increasing angle. To overcome this difficulty we can turn a physical pendulum into a so-called reversible (Kater's) 1 pendulum. In the experiment the acceleration due to gravity was measured using the rigid pendulum method. The period, \(T\), of a pendulum of length \(L\) undergoing simple harmonic motion is given by: \[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]. Theory The period of a pendulum (T) is related to the length of the string of the pendulum (L) by the equation: T = 2 (L/g) Equipment/apparatus diagram 1 We first need to find the moment of inertia of the beam. The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty. The magnitude of the torque is equal to the length of the radius arm times the tangential component of the force applied, |\(\tau\)| = rFsin\(\theta\). An example of data being processed may be a unique identifier stored in a cookie. Now for each of the 4 records, we have to calculate the value of g (acceleration due to gravity)Now see, how to calculate and what formula to use.we know, T = 2(L/g) => T2 = (2)2 (L/g) => T2 = 42 (L/g) (i) => g = 42 L / T2 (ii) [equation to find g]. The restoring torque is supplied by the shearing of the string or wire. Pendulum | Definition, Formula, & Types | Britannica To Find the Value of Acceleration Due to Gravity (g), Radius of By timing 100 or more swings, the period can be determined to an accuracy of fractions of a millisecond. DONATE on this QR CODE or visit ALE Donations for other payment methods, Coaching WordPress Theme - All Rights Reserved, To Determine the Value of Acceleration Due to Gravity (g) Using Bar Pendulum. /F1 6 0 R 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. % (adsbygoogle = window.adsbygoogle || []).push({});
. A bar pendulum is a particular case of a compound pendulum. /ProcSet [/PDF /Text ] Discussion and calculations of compound pendulum due to gravity %PDF-1.5 15.5: Pendulums - Physics LibreTexts A simple pendulum is defined to have a point mass, also known as the pendulum bob, which is suspended from a string of length L with negligible mass (Figure \(\PageIndex{1}\)). 3 0 obj What It Shows An important application of the pendulum is the determination of the value of the acceleration due to gravity. Save my name, email, and website in this browser for the next time I comment. The units for the torsion constant are [\(\kappa\)] = N m = (kg m/s2)m = kg m2/s2 and the units for the moment of inertial are [I] = kg m2, which show that the unit for the period is the second. 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. Here, the only forces acting on the bob are the force of gravity (i.e., the weight of the bob) and tension from the string. stream >> A string is attached to the CM of the rod and the system is hung from the ceiling (Figure \(\PageIndex{4}\)). Your email address will not be published. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). Which is a negotiable amount of error but it needs to be justified properly. To analyze the motion, start with the net torque. 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. Surprisingly, the size of the swing does not have much effect on the time per swing . 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. Pendulum 1 has a bob with a mass of 10 kg. Note that for a simple pendulum, the moment of inertia is I = \(\int\)r2dm = mL2 and the period reduces to T = 2\(\pi \sqrt{\frac{L}{g}}\). iron rod, as rigidity is important. We built the pendulum with a length \(L=1.0000\pm 0.0005\text{m}\) that was measured with a ruler with \(1\text{mm}\) graduations (thus a negligible uncertainty in \(L\)). This is consistent with the fact that our measured periods are systematically higher. PDF Measurement of acceleration due to gravity (g) by a compound pendulum Start with the equation from above Square both sides to get Multiply both sides by g Divide both sides by T 2 This is the equation we need to make our calculation.
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