Academia.edu no longer supports Internet Explorer. Therefore the length H of the pendulum is: $$ H = 2L = 5.96 \: m $$, Find the moment of inertia for the CM: $$I_{CM} = \int x^{2} dm = \int_{- \frac{L}{2}}^{+ \frac{L}{2}} x^{2} \lambda dx = \lambda \Bigg[ \frac{x^{3}}{3} \Bigg]_{- \frac{L}{2}}^{+ \frac{L}{2}} = \lambda \frac{2L^{3}}{24} = \left(\dfrac{M}{L}\right) \frac{2L^{3}}{24} = \frac{1}{12} ML^{2} \ldotp$$, Calculate the torsion constant using the equation for the period: $$\begin{split} T & = 2 \pi \sqrt{\frac{I}{\kappa}}; \\ \kappa & = I \left(\dfrac{2 \pi}{T}\right)^{2} = \left(\dfrac{1}{12} ML^{2}\right) \left(\dfrac{2 \pi}{T}\right)^{2}; \\ & = \Big[ \frac{1}{12} (4.00\; kg)(0.30\; m)^{2} \Big] \left(\dfrac{2 \pi}{0.50\; s}\right)^{2} = 4.73\; N\; \cdotp m \ldotp \end{split}$$. As in the Physical Pendulumdemo, the pendulum knife-edge support is a U-shaped piece of aluminum that is clamped onto a standard lab bench rod. In this channel you will get easy ideas about Physics Practical Classes. /F8 27 0 R A 3/4" square 18" long 4 steel bar is supplied for this purpose. Using a simple pendulum, the value of g can be determined by measuring the length L and the period T. The value of T can be obtained with considerable precision by simply timing a large number of swings, but comparable precision in the length of the pendulum is not so easy. This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. /F7 24 0 R The angular frequency is, \[\omega = \sqrt{\frac{mgL}{I}} \ldotp \label{15.20}\], \[T = 2 \pi \sqrt{\frac{I}{mgL}} \ldotp \label{15.21}\]. But note that for small angles (less than 15), sin \(\theta\) and \(\theta\) differ by less than 1%, so we can use the small angle approximation sin \(\theta\) \(\theta\). 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. A bar pendulum is a particular case of a compound pendulum. Rather than measure the distance between the two knife edges, it is easier to adjust them to a predetermined distance. Several companies have developed physical pendulums that are placed on the top of the skyscrapers. 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. A physical pendulum with two adjustable knife edges for an accurate determination of "g". Even simple pendulum clocks can be finely adjusted and remain accurate. The following data for each trial and corresponding value of \(g\) are shown in the table below. 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}}: \[I \alpha = \tau_{net} = L (-mg) \sin \theta \ldotp\]. /MediaBox [0 0 612 792] Some of our partners may process your data as a part of their legitimate business interest without asking for consent. We suspect that by using \(20\) oscillations, the pendulum slowed down due to friction, and this resulted in a deviation from simple harmonic motion. A rod has a length of l = 0.30 m and a mass of 4.00 kg. Read more here. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 1 Objectives: The main objective of this experiment is to determine the acceleration due to gravity, g by observing the time period of an oscillating compound pendulum. 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. Non-profit, educational or personal use tips the balance in favour of fair use. Consider a coffee mug hanging on a hook in the pantry. Like the simple pendulum, consider only small angles so that sin \(\theta\) \(\theta\). The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 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. 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. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12. Required fields are marked *. Enter the email address you signed up with and we'll email you a reset link. This was calculated using the mean of the values of g from the last column and the corresponding standard deviation. /F10 33 0 R The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. As with simple harmonic oscillators, the period T for a pendulum is nearly independent of amplitude, especially if \(\theta\) is less than about 15. Kater's pendulum, shown in Fig. The mass, string and stand were attached together with knots. We plan to measure the period of one oscillation by measuring the time to it takes the pendulum to go through 20 oscillations and dividing that by 20. [Caution: Students are suggested to consult Lab instructors & teachers before proceeding to avoid any kind of hazard.]. /F6 21 0 R This removes the reaction time uncertainty at the expense of adding a black-box complication to an otherwise simple experiment. Note the dependence of T on g. If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity, as in the following example. This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format
The object oscillates about a point O. We have described a simple pendulum as a point mass and a string. Best on the results findings, it showed that the Rafin Tambari has the highest value of acceleration due to gravity which is (10.2 m/s 2). A solid body was mounted upon a horizontal axis so as to vibrate under the force of gravity in a . Any object can oscillate like a pendulum. /Font << The length should be approximately 1 m. Move the mass so that the string makes an angle of about 5 with the vertical. We transcribed the measurements from the cell-phone into a Jupyter Notebook. 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. We thus expect that we should be able to measure \(g\) with a relative uncertainty of the order of \(1\)%. We can then use the equation for the period of a physical pendulum to find the length. %PDF-1.5 To overcome this difficulty we can turn a physical pendulum into a so-called reversible (Kater's) 1 pendulum. 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. 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. The compound pendulum is apt at addressing these shortcomings and present more accurate results. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. 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. A digital wristwatch or large analog timer 3 is used to verify the period. In this video, Bar Pendulum Experiment is explained with calculatio. The period is completely independent of other factors, such as mass. University Physics I - Mechanics, Sound, Oscillations, and Waves (OpenStax), { "15.01:_Prelude_to_Oscillations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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